One of the first questions you should ask is whether or not Google Compute, or even the Google Toolbar, are adware or spyware. While a purist would argue that anything falls into that category, we do not believe these are beyond the normal "Google sees all" that goes on anyway ... and they are very clear about what they do and don't do, versus a lot of software that is downright sneaky.
Another good question is does this slow down my PC? According to this report, there is very minimal impact to your PC, basically they found less than a 1% performance hit while running the most demanding games since it is the lowest priority task and throttles back whenever you need more power. It is not even noticeable for normal tasks on modern day hardware. Generally running 2 applications takes less than 10% of your processor's power most of the time. You should note that your CPU chip never gets a chance to "throttle down" unless you change a setting, so especially on notebooks, so things will probably "hum along" a bit more than before you installed Google Compute.
Finally, here is the FAQ from Google about the Google Compute project that give a good overview and addresses various issues such as privacy, spy-ware, performance, and how you can easily turn it off or uninstall completely if you need to.
Main powder2glass Google Toolbar Compute Page