"Is any ATX PSU compatible with a 2U server chassis?"
Yes, but barely any, and it depends completely on the chassis in question; even then most will require hacking the chassis to get a desktop PSU to fit.
Judging by the images of the chassis you want to use, a desktop ATX is not going to fit with a full size board in it (note how long the example PUS is in comparison to its width).
Basically you'll need to test fit, and be prepared to start hacking at the metal.
Additionally, many server-grade motherboards don't work with a desktop PSU due to lack of additional power needs, and sometimes different wiring needs. Confirm you board can run with a standard desktop ATX PSU first.
Lastly, 2U chassis are TIGHT for space, if you go over the expected sizes in the slightest, things won't fit under the lid. This often leads to requiring use of specific parts/form factors, to make it all fit.
"Do I have to care about the side of the PSU where the fan is (see the photo above) being blocked by the top panel of the server chassis?"
Since that fan is the primary intake (of fresh air) for cooling the PSU, then yes, you need to worry about blocking it.
Note most/all Rack chassis PSU's implement front-to-back air-flow, since they are intended to be stacked in a rack with other chassis, with no air gap above or below.