From a purely theoretical perspective, you are considering a two-photon state of the form $|2\rangle\equiv\frac{1}{\sqrt2}(a^\dagger_\psi)^2|0\rangle$ where $a_\psi^\dagger=\sum_k c_k a_k^\dagger|0\rangle\equiv\sum_k c_k |k\rangle$ creates a single-photon state that is a superposition of a bunch of spatial mode (think of $\psi$ as the wavepacket of the photon).

So now you are asking: suppose you can detect independently single-photon absorption at different modes. I'd model this as asking what are the probabilities
$$\langle 1_i 1_j|2_\psi\rangle\equiv
\langle 0|a_i a_j \frac{1}{\sqrt2}(a_\psi^\dagger)^2|0\rangle
= \frac{1}{\sqrt2}\sum_{k\ell} c_k c_\ell \langle a_i a_j a_k^\dagger a_\ell^\dagger\rangle
= \frac{1}{\sqrt2}\sum_{k\ell} c_kc_\ell (\delta_{ik}\delta_{j\ell}+\delta_{i\ell}\delta_{jk})
= \sqrt2 c_i c_j.$$
It follows that the probability of detecting a coincidence on two different modes $i,j$ is $p(i,j)=2 |c_i c_j|^2$, where $|c_i|^2$ is the probability of finding $a_\psi^\dagger$ in the $i$-th mode.

In other words, on paper, sure, this is possible. I'm not aware of this having been directly observed experimentally though. The thing is that single-photon detectors generally cannot resolve different spatial modes within a single-photon beam, and *vice versa*, pixel-resolving devices (such as CCD cameras) generally only detect intensities. The technology to do pixel-resolving single-photon detectors is relatively recent, and still under active development. See *e.g.* https://arxiv.org/abs/2007.16037 for some discussion of recent developments in this field.