Like the subject says, can it be done?
I don't think so, and I don't think trying to do so is a Good Idea™©®, see below...
Yes, and the result was a completely borked OS, followed by a complete re-install. Now, I admit that this was a long time ago on an older Fedora release, and maybe I fumbled the operation, but... I repeat: I don't think that this is a very good idea - too many things can go so very wrong.
, simply switching to a 32-bit PAE kernel will solve the RAM issue.
P.S. Note that switching major hardware (such as the MoBo) may result in a non-bootable OS, as the drivers in the kernel boot image may not be correct for the new iron, especially considering what you have stated (32-bit to 64-bit board). Or, you may get lucky. This time. At worst, you boot a live CD/DVD and re-build the initramfs image(s).