This paper by Lubini et al. suggests that the answer to your question is "no": arxiv.org/abs/1104.2851v2. Lubini et al. consider the weak-field limit of $f(R)$ gravity where matter that contributes to spacetime curvature is assumed to be non-relativistic (Lubini et al. say at one point that they are assuming the spacetime is stationary. But this is not necessary; it is only necessary to assume that the matter contributing to the stress-energy tensor has velocities small compared to c). These assumptions should provide a good approximation for clusters and cluster collisions including the Bullet Cluster which has an impact velocity of ``only'' about 1% of the speed of light (see arxiv.org/abs/1307.0982).

The field equation resulting from varying the metric in the $f(R)$ action involves $f(R)$ and $f'(R)$. Lubini et al. assume that $f(R)$ in analytic in $R$ at $R=0$ so that in the weak field limit $$f(R) \approx f(0) + f'(0)R$$ and $$f'(R) \approx f'(0) + f''(0)R.$$ Lubini et al. show that in the weak-field limit the metric is given by (setting $G=c=1$) $$ds^2 = -(1-h_{00})dt^2 + \delta_{ij}(1 + h)dx^idx^j$$ where $$h_{00}({\bf x},t) = -2\Bigl(\Phi({\bf x},t) + \frac{1}{3}\Psi({\bf x},t)\Bigr),$$ $$h({\bf x},t) = -2\Bigl(\Phi({\bf x},t) - \frac{1}{3}\Psi({\bf x},t)\Bigr),$$ $\Phi({\bf x},t)$ is the Newtonian potential given by $$\Phi({\bf x},t) = -\int\frac{\rho({\bf x}',t)}{|{\bf x} - {\bf x}'|}d^3x',$$ and $\Psi({\bf x},t)$ is a "massive" scalar field given by the Yukawa form $$\Psi({\bf x},t) = -\int\frac{\rho({\bf x}',t)}{|{\bf x} - {\bf x}'|}e^{-a|{\bf x} - {\bf x}'|} d^3x'$$ where $$a^2 = \frac{f'(0)}{3f''(0)}.$$

$\Psi({\bf x},t)$ is the effectively massive scalar mode contained in $f(R)$ theories that is not contained in general relativity. The motion of a massive, non-relativistic particle is determined in terms of $h_{00}$ which depends on the additional scalar field $\Psi({\bf x},t)$. However, the motion of massless particles (e.g., photons) is determined by the combination $h_{00} + h$ which according to the above equations is independent of $\Psi({\bf x},t)$. Lubini et al. show that the motion of photons depends only on $h_{00} + h$ in the weak-field limit by calculating an effective refractive index. This is done by noting that according to classical geometric optics the trajectory of a photon extemizes the quantity $t = \int n dl$ where $n$ is the refractive index and $l$ is a spatial length along the path of the photon. The above metric implies that along a null geodesic $$dt^2 = \frac{1+h}{1-h_{00}}dl^2 \approx (1 + h + h_{00})dl^2$$ and therefore in the weak-field limit the effective refractive index is $$n = 1 + \frac{1}{2} (h + h_{00}).$$ Since this does not depend on $\Psi({\bf x},t)$, gravitational lensing is not affected by $\Psi({\bf x},t)$ in the weak-field limit and is given by the standard general relativity result in this limit.

The deflection of light can also be determined using the geodesic equation. This is done by Stabile and Stabile: arxiv.org/abs/1108.4721v2. Stabile and Stabile confirm Lubini et al.'s results for $f(R)$ theories and they also consider $f(R,R^{ab}R_{ab})$ theories. They conclude that $f(R,R^{ab}R_{ab})$ theories can alter the general relativity prediction for gravitational lensing, but that the lensings is suppressed so that even more dark matter would be needed to explain the observed lensing.

So, in summary, it seems unlikely that the additional scalar mode of $f(R)$ theories could explain gravitational lensing without dark matter since in the leading order correction to general relativity, the trajectory of photons is not affected by the additional scalar mode.

This paper by Lubini et al. suggests that the answer to your question is "no": arxiv.org/abs/1104.2851v2. Lubini et al. consider the weak-field limit of $f(R)$ gravity where matter that contributes to spacetime curvature is assumed to be non-relativistic (Lubini et al. say at one point that they are assuming the spacetime is stationary. But this is not necessary; it is only necessary to assume that the matter contributing to the stress-energy tensor has velocities small compared to c). These assumptions should provide a good approximation for clusters and cluster collisions including the Bullet Cluster which has an impact velocity of "only" about 1% of the speed of light (see arxiv.org/abs/1307.0982).

The field equation resulting from varying the metric in the $f(R)$ action involves $f(R)$ and $f'(R)$. Lubini et al. assume that $f(R)$ in analytic in $R$ at $R=0$ so that in the weak field limit $$f(R) \approx f(0) + f'(0)R$$ and $$f'(R) \approx f'(0) + f''(0)R.$$ Lubini et al. show that in the weak-field limit the metric is given by (setting $G=c=1$) $$ds^2 = -(1-h_{00})dt^2 + \delta_{ij}(1 + h)dx^idx^j$$ where $$h_{00}({\bf x},t) = -2\Bigl(\Phi({\bf x},t) + \frac{1}{3}\Psi({\bf x},t)\Bigr),$$ $$h({\bf x},t) = -2\Bigl(\Phi({\bf x},t) - \frac{1}{3}\Psi({\bf x},t)\Bigr),$$ $\Phi({\bf x},t)$ is the Newtonian potential given by $$\Phi({\bf x},t) = -\int\frac{\rho({\bf x}',t)}{|{\bf x} - {\bf x}'|}d^3x',$$ and $\Psi({\bf x},t)$ is a "massive" scalar field given by the Yukawa form $$\Psi({\bf x},t) = -\int\frac{\rho({\bf x}',t)}{|{\bf x} - {\bf x}'|}e^{-a|{\bf x} - {\bf x}'|} d^3x'$$ where $$a^2 = \frac{f'(0)}{3f''(0)}.$$

$\Psi({\bf x},t)$ is the effectively massive scalar mode contained in $f(R)$ theories that is not contained in general relativity. The motion of a massive, non-relativistic particle is determined in terms of $h_{00}$ which depends on the additional scalar field $\Psi({\bf x},t)$. However, the motion of massless particles (e.g., photons) is determined by the combination $h_{00} + h$ which according to the above equations is independent of $\Psi({\bf x},t)$. Lubini et al. show that the motion of photons depends only on $h_{00} + h$ in the weak-field limit by calculating an effective refractive index. This is done by noting that according to classical geometric optics the trajectory of a photon extemizes the quantity $t = \int n dl$ where $n$ is the refractive index and $l$ is a spatial length along the path of the photon. The above metric implies that along a null geodesic $$dt^2 = \frac{1+h}{1-h_{00}}dl^2 \approx (1 + h + h_{00})dl^2$$ and therefore in the weak-field limit the effective refractive index is $$n = 1 + \frac{1}{2} (h + h_{00}).$$ Since this does not depend on $\Psi({\bf x},t)$, gravitational lensing is not affected by $\Psi({\bf x},t)$ in the weak-field limit and is given by the standard general relativity result in this limit.

The deflection of light can also be determined using the geodesic equation. This is done by Stabile and Stabile: arxiv.org/abs/1108.4721v2. Stabile and Stabile confirm Lubini et al.'s results for $f(R)$ theories and they also consider $f(R,R^{ab}R_{ab})$ theories. They conclude that $f(R,R^{ab}R_{ab})$ theories can alter the general relativity prediction for gravitational lensing, but that the lensings is suppressed so that even more dark matter would be needed to explain the observed lensing.

So, in summary, it seems unlikely that the additional scalar mode of $f(R)$ theories could explain gravitational lensing without dark matter since in the leading order correction to general relativity, the trajectory of photons is not affected by the additional scalar mode.