Quite a few websites have actually tried this. There's actually two elements I'd consider here - whether the task you are doing is processor bound, and whether the PCIe bus has enough bandwidth for what you are trying to do.
Both hot hardware and toms hardware did tests on older CPUs and newer GPUs - specifically core 2s. Tom's hardware covered more CPUs... and when they tried borderlands 2
Each processor delivers a nice playable experience at Medium settings.
However, a couple of those downward spikes near the beginning of the
run corresponded to a brief, yet still noticeable stutter.
Hot hardware also found that you could push graphics settings higher with a new GPU and an older CPU. If you can run a game, the new GPU will definately improve your experience. These tests indicate that unless you're throwing in a seriously high end video card, you shouldn't be getting bitten in the rear by either CPU usage or PCIe Bandwidth, and you should be seeing better performance. In the context of a longer term build, it makes sense to do this.