Not really.
You want to calculate the probability to find all the molecules in the left half of the volume.
Since the probability density is
$$\rho(\{q,p\}) = c_N \frac{e^{-\beta H(\{q,p\})}}{\Omega(U,V,N)}\ ,$$
where, $c_N$ is a constant and, to ensure the normalization, $$\Omega(U,V,N ) = c_N\int e^{-\beta H(\{q,p\})} dq^{3N} dp^{3N}$$
what you need to consider is
$$\text{Pr} =\int_{\{q,p\}_{V/2}} \rho (\{q,p\}) dq^{3N} dp^{3N} = c_N \frac{ \int_{\{q,p\}_{V/2}} e^{-\beta H(\{q,p\})} dq^{3N} dp^{3N}}{\Omega(U,V,N)}$$
where $\{q,p\}_{V/2}$ is the set of coordinates such that all the molecules are in the left half of the volume.
You can immediately see that
$$c_N \int_{\{q,p\}_{V/2}} e^{-\beta H(\{q,p\})} dq^{3N} dp^{3N} = \Omega(N,V/2,U)$$
So that you finally obtain the desired result.