Will it bottleneck ?

Depends on what you're doing with it. I think a lot of people use the term "bottleneck" with limited understanding of varying factors.

A 6770 is a 2 or 3 generations old entry level graphics card. What exactly are you trying to do with it? The question is too generic.
 
That still doesnt answer the question. Some games are more demanding than others, resolutions and game settings have to be considered as well, including your own expectations. For playing a game like Runescape, yea that system is "OP" for that.. For Battlefield 4 at ultra settings, full AA and 1920x1080 resolution, that system will fall flat on its face.