While the x4 830 may not be as powerful as a current generation processor, it is a 3.2GHz quad core and still fairly powerful.
While you may have some bottlenecking in CPU dependent games, I would see no issues in paring a GTX 660Ti with it.
If anything, overclocking your CPU would go a long way to removing any potential bottlenecks.
Yes, this would go a long way towards mitigating any possible bottleneck.
Any bottlenecks will depend on the specific game.
Depending on what you are playing, it could be that the GPU would already be the bottleneck.
Worst case though, a GTX 660Ti will still give you a healthy performance increase over your current GTX 550Ti
I have a 7950 with a 1090t @ 3.6ghz and the only game that has bottlenecking issues from what I have seen is crysis 2. And it really isn't that big of a deal either (the gpu can only reach 96% usage). You will be fine with your cpu and a 660ti, although I would advise getting a 7870 because of the price cuts they will be getting soon.
IMO, the minimal performance increase from upgrading to an x4 965 would not justify the costs.
If you are not happy with your performance after upgrading the GPU it would be best to save you CPU budget towards a new platform some time in the future.