Can a GPU be bottlenecked?

Can a GPU, let's say anything between HD6770 and HD7970GE, be bottlenecked in GUIMiner due to a slow platform? Will an Intel Atom or AMD E-series APU affect the GPU hash rate?

If I am to build a 24/7 Bitcoin machine, it'll have to be as low-power as possible.

The 7900 series won't have that good of an increase in hash rate, anyway. The 5800 series is where it's at; for mining, the 5800 series gets rediculous hash rates, and they are really cheap. 

But, if you already have the 7970 that's going in, then there may be a bottleneck. In gaming, it would be noticable, but outside of that, in mining, you should be fine. 

I'm talking about a dedicated Bitcoin machine to run 24/7. Nothing else.

Example; can I throw my HD6870 in a system with AMD E-350 platform and still maintain 275 Mhash/s? Or will the GPU be bottlenecked and drop?