Yes it will bottleneck if and only if all utilized cpu cores are maxed out by an application.
Basically it comes down to the game. You won't get stutters usually, it just means that your graphics card will run cooler and idle more often.
You will get a lower framerate from the CPU being a bit slower too, but the impact isn't really noticeable honestly.
If a game can utilize all of your cores, then you should be fine for most of those games. Just think about it like this. As long as your CPU meets the requirements+, you'll be fine, and this card will be great for the future if you decide to get a better CPU.