Not exactly. The Classic ROM is a single chip whereas the SE had two chips (like the Plus before it). In much the same way the Classic II had 2 chips on the early models and 4 chips on the later models. (Would be curious if those Classic II chips are swappable with an earlier Mac.) It almost seems like Apple intentionally varied the ROM configurations to prevent exactly this kind of thing.
I suppose it would be possible to swap ROMs with a custom socket re-map, but you'd need the pinouts of both the SE & and the Classic to adapt the Classic's 40 pin ROM to the SE's combined 56 pins. Likely more trouble than simply swapping the logicboard. The embeded System is nice but not really a practical addition to an SE if you're just trying to keep PDS expansion options. Also, there may be a custom IC on the Classic's logicboard which is required by the ROM to boot. i.e. it might hang on the SE waiting for confirmation of the chip, then again it may not. It is a minor variation of code I am told by the Mini vMac Classic emulator developer specifically to support the backlight CDEV like the Portable. But otherwise they are identical.
EDIT:
I have only read that there were Classic II 2 & 4 chip ROM boards, however, I have NEVER seen one or seen any official Apple documentation that references them. Anyone who can confirm the existence of the 2 chip ROM board would be appreciated. This posting from Apple is as close as I've come, but it's way off showing the 2 & 4 chip variations for the original Classic which had only one chip. http://docs.info.apple.com/article.html?artnum=11609