It is highly dependent on the game.
For example with Battlefield: Vietnam, I had to take my AthlonXP down to 1200 MHz before I saw FRAPS framerates decrease at all in a range that was below the refresh rate of my monitor, but BFV is one of the least CPU dependent games I know of. Other games will see a more significant difference.
You have to guess to some extent. But looking at pages like this (latest AT article I could find that included the AXP):
http://www.anandtech.com/cpuchipsets/showdoc.aspx?i=2275&p=10
You can see some examples of a few games that show a significant decrease in performance with the AXP. From the framerate information you can gather how close it is to 'acceptable' performance. For example in a game like BFV, where an AXP 3200+ is scoring 170 FPS, you have a ways to go before it's actually going to limit your performance (because you will set video options that will have a lower average framerate, probably in the 30-60 FPS range). But in games like Doom3, where the AXP 3200+ is showing 58, you have less margin before the CPU becomes the bottleneck.
The thing to realize about the CPU bottleneck is that it will be there no matter what video card you have. The worst you can do with a new card is about the performance you are getting now with your current card but at higher resolution and/or video quality settings. This is because CPU demands generally do not increase much, if at all, with increasing resolution and/or video quality settings.
I see nothing wrong with upgrading your video card and rolling the dice on the CPU bottleneck. If it's not the bottleneck, you clearly gain. If the CPU is indeed the bottleneck you STILL get a visual quality improvement unless you are currently already gaming at the max monitor resolution, and you can upgrade your CPU platform at a later date. The only thing you can't guarantee with a good video card upgrade is that you will see a speed improvement. Visual quality/resolution improvement is a guarantee.
You can use your game to verify if your CPU is the primary factor by scaling the resolution down a notch and seeing if performance gets a significant improvement. If performance does not significantly improve, it is likely a CPU issue. If it does, your GPU is limiting in your current games and you can verify you will get a speed AND quality improvement with a GPU upgrade.