I've put all the compact logicboards and analogue boards, except the CC, in an original M0001 case. All you need are the pinouts to go from one power supply to the other. The main difference in the later compacts is that they provided additional power for things like PDS cards, hard drives and the like. Though the SE does not run its audio through the power board.
The reverse is likely true, but LCGuy makes a valid point. You will not be able to put a pre-Classic board into a Classic case without more or less gutting it and altering the rear case port access. Also, you will not be able to use the SE's sound without modifying the Classic's audio circuitry. You will not be able to adjust the brightness of the Classic monitor. But the board should otherwise work. You will need to make sure a fan is installed in the case. Finally, using the existing Classic chassis, you won't be able to use any expansion cards. The logicboard rails will have to be modified and the current height may also not be enough to accommodate the SE/30's SIMMs.
It's definitely a major hack to put a functional SE/30 in there. Easier to put the Classic II in an SE/30 case or transplant the entire guts from the SE/30 and not try to mix them.