Here's what will REALLY HAPPEN:
As the rear channels often don't receive that much info (and if they do, it's usually for intermitent periods of time), usually things will "run" fine back there, in terms of delivering a steady flow of power. Mind you however that, depending on where the power is hitting the speakers (what frequency ranges are being stressed with information), the sound will tend to flatten out in some respects, limiting dynamics and fullness to the sound. Basically, there's more, and the amps, yes will either start to get hot or, in extreme cases, shut down! You could easily do this running two 4 ohm speakers (of modest sensitivity) running full range, if you ran them in a 2 channel stereo configuration. You couple that with the fact that receivers offer limited dynamics, flatter sound, more strainned and constricted soundstage in comparison to separates amp set-up's most often, and you just have to consider the sonic compromises that would be pressent.
If it where me, I'd MOST DEFINITELY be adding a multi-channel amp to run your system, at the very least!!!
I've done receiver setups for years, and they simply CANNOT compete in terms of sound quality over a good separates amp application. And that includes the large Denon's, Marantz's, B&K's, etc!
So, just ask yourself what level of sonic performance is acceptable, and go that route. For me, I'd not hesitate to forget the amps in those receivers, and get some REAL amplification!! (at the very least you owe it to yourself to try another amp in the system connected to your receiver running as a pre-pro, to compare).
Note, however, that running all your (even 4 ohm) speakers as "small", will help things greatly in terms of efficiency for your system which, yes, will help. Good luck
