Will i5 2310 bottleneck gtx 1060 3gb

Solution
Your 1060 will be just fine at 1080p. That i5 will start to show it's age in a couple of years, especially considering it's a lower tier one. But for now, it should be good. If you're going to be playing AAA titles, then you do have a problem in the RAM department. 8gb is minimum now a days, but 12gb would be preferred. That would be the first thing I would look at upgrading when the time comes. Hope that helped.
Maybe, depends on game. Your limiting factor isn't the CPU or GPU, its going to be your RAM as 4gb really isn't enough for gaming. Even if the i5 does hold back the GPU a little bit it's still much better then no GPU at all but if your still in the buying process I'd recommend getting a GTX 1050 ti and using the rest of your budget for more RAM.
 
Your 1060 will be just fine at 1080p. That i5 will start to show it's age in a couple of years, especially considering it's a lower tier one. But for now, it should be good. If you're going to be playing AAA titles, then you do have a problem in the RAM department. 8gb is minimum now a days, but 12gb would be preferred. That would be the first thing I would look at upgrading when the time comes. Hope that helped.
 
Solution
You should be fine however as other stated I would say it would be better to use the difference in money you were going to spend on the 1060 3GB, get a 1050 TI instead and use that money to upgrade your system ram.