Will it bottleneck it?

Disagree with above on both points.

Even the older and weaker i3 4130 runs Fallout 4 at acceptable fps, yes its bottlenecking but it still plays well. This game is fairly cpu heavy http://www.gamersnexus.net/game-bench/2182-fallout-4-cpu-benchmark-huge-performance-difference

As for getting a 1060 then to spend on a 1070 later, that's just a major expense for not enough gain. I'm guessing as this is a budget build this will be used with a 1080p or less monitor which the 1060 can run all games at very high settings.

For a budget gaming build the 6100 & 1060 are a frequently recommended pairing. Obviously an i5 is better but if budget doesn't allow for then the i3 is acceptable.