It's not that the CPU will degrade your GPUs performance, it's that you have to balance the performance of the games themselves. For example, if your CPU is equal to or better than the "recommended" CPU for that game, then you won't have a bottleneck per se...but since the game probably won't stress the 380, you'll be able to turn all of the quality settings up to '11'. If your CPU is somewhere between "minimum" & "recommended", then depending on the game you may have to fine-tune some of the most advanced settings, but depending on resolution you should still be able to hit 60+ FPS with just about any game on "high"or "ultra" levels. If your CPU is barely above "minimum" for the game...that's where a "bottleneck" may occur, in the sense that your CPU just can't get the data to your GPU fast enough for it to crunch it.
What's your current GPU, & what games will you be playing?