if it has the same characteristics yes, you can probably get away with it
but ripple of any kind could make the cpu do wonky things, and is why they use several MOSFETs and caps in parallel.
Worst case scenario, as little as +.1V can fry it
Then again, I've seen aging Pentium 4 boards with venting caps just keep going (why won't you die damnit!) So YMMV.
Obviously this board is a bit more sensitive since it isn't posting.
Now, I'm curious as to how you were getting a error message at all considering a short on the 12V line would have the ATX supply trip. damned OEM equipment.