You would still hit a bit of a bottleneck, though not nearly as bad as with your old Core 2 Duo. The FM2 Athlon II CPUs aren't particularly fast, and they lack L3 cache which will hurt their game performance somewhat, they are budget chips meant to be run with their integrated graphics and/or an entry level graphics card. If you want an AMD chip, I would recommend an FX 6300 at minimum or an FX 8350 if you can afford it. With Intel, don't get anything less than an i5, as newer games are starting to have trouble with running at full settings with a dual core CPU.
If you lack the funds for a full rebuild right now, you can just grab the new graphics card now, and stick it in the new build later when funds become available, just don't expect to get the full performance out of your new card with your current system.