The SE, SE FDHD (aka SuperDrive) and SE/30 logic boards are all interchangeable, so it should work.
The SuperDrive floppy mechanism will work with the SE logic board, but it'll only read/write 800k floppies.
The analog board/power supply is also interchangeable. In fact, pretty much everything is. They're all quite similar (aside from the logic board, the differences are mostly cosmetic).
Another thing to try is to decrease the brightness until the screen is just barely visible and see if things get better. If the clicking and distortions stop or decrease then then caps are suspect. Lowering the brightness lowers the stress on the analog board components.