There should be no problem with this, providing the PSU is powerful (which it should be). You may not be able to do much over clocking either. You may also run into issues under heavy CPU load and the machine potentially could just turn off!
Other people have reported this successfully too (http://www.overclock.net/t/1158071/4-pin-power-supply-on-8-pin-motherboard).
The question should be, which side you connect it too!
You don't NEED to use all 8 pins for the EPS-12v. That's just in case
you wan't to feed the CPU more power if it needs it.
If it has a 8-pin you can connect the 4 pins to one side of the
connector, depending on where your motherboard manual says to.
You may want to buy an adapter though which will 'update' it from 4 pin to 8 pin (recommended) or waiting until you get the new PSU but, that's just me being cautious!
Some times you can email the motherboard manufacturer though if you're worried about this before doing it!