From the view point of information loss we can think about how many degrees of freedom there are. The detector will in general have few degrees of freedom (compared to the source system you are trying to measure) and that is even if its precision is perfect!
Now let me try to specifically address the points in your question wether we could see
see behind objects ?
information encoded by the photons.
What you would try to use is either diffraction (i.e. so that the photons get to the detector around corners) or reflection (photon bouncing off a wall).
Reflection is easily discarded as a process to see objects around the corner: Take a perfect mirror and your detector sees the photons coming from it. How is going to know wether something bounced off at that point or simply came from further behind? (of course if you knew a priori that it is a mirror you could maybe infer that, but that is really not the point of this question.
Diffraction is a bit harder to see. All the diffractive systems I have encountered have a finite number of modes (i.e. when coupling to any detector, not just practical ones) passing through the system with significant efficiency/throughput. I am just gonna name an example that I simulated: for a grating spectrometer I got about 20... and there is know way you reconstruct any object from 20 pieces of information (number).
To summarize: what I argued here is that this is not possible from a purely theoretical viewpoint due to degeneracy in the optical propagation and the resulting information loss about the source. So I would say we can most certainly take the answer to be: no, this is not possible in general, you can't fully reconstruct an object around the corner! The "in general" of course means on the other hand that you might be able to do it for specific sources/environments that you are looking at. And the "fully" means you might be able to partially reconstruct it. But I think what I can say is: You can not see around corners in general, no matter how good you make your detector!