Effect of disabling onboard graphic

Would there be any problem (performance-wise or otherwise) to disable the onboard GPU and use a discreet card like ATI HD 4770 instead?

To be honest, I'd avoid the 4770. It's a pretty mediocre card for gaming by today's standards.

If you get an AM3 chip, the 4870 or 4890 is better matched to its power. You might even consider a 5770 if you're planning on keeping the machine for a few years, since it had DirectX 11 and the 4xxx cards don't.

Well the 48XX series is faster than the 4770 But it is also older, hotter technology that uses more power. The 48XX series are 55nm. They are also discontinued.

The 4770 is about almost as fast as a 4850 but it's a newer 40nm design, which runs cooler and uses less power. A pair of 4770's would be a decent setup but I dont know if you would even be able to find any 47xx or 48xx in a year or so.

If you plan on just getting a newer card in a year or two instead of crossfiring, then the 4870 1GB is the best deal going. The GTX260 is also very good.
Seriously I recommend always getting the fastest single card you can afford rather than crossfiring older cards together. It creates more heat and likely you'll need a better power supply to add another card so I would seriously reconsider the crossfire and save some money by going with the 785G.