umm, the voltage coming out of the rectifying bridge is going to be about the RMS voltage of AC, which is around 170 volts. if you feed 12 volts into a power supply that is expecting 170 volts, it is not going to work.
think about it, that'd be like putting 1 volt into a DC-DC that is designed to have a 12 volt input, and expecting it to work. Sure, it would be possible with some form of design, but a standard power supply is NOT going to be built to accept some insanely large input range, since it would never have to in normal use, and it would be far more expensive to make it that versatile.
as for bypassing the main transformer... well sure, it'd work if there were a transformer with a 12v-ish output that was running the PSU. BUT the whole point of a SWITCHING power supply is that it doesn't use a giant transformer, rather it switches down the high rectified voltage directly. think about it, a 500 watt power supply would need a hella big transformer if that were the case.
don't mean to dash your hopes here, but given the number of people with electronics skills on this board, I'm sure someone would have done it by now if it were possible.