Will a i3-4130 bottleneck a GTX 1070

Solution
Yes the i3-4130 would definetly bottleneck a GTX 1070. The minumim for a 1070 imo is a i5 3570/k. You should upgrade to a 4th gen i5 or i7 soon.
There is no general answer. Some games are highly GPU dependent, some are highly processor dependent and some need both.
From the processor side, Some games prefer fewer but faster cores, some prefer more cores...and so on....
But....i3 could already bottleneck GTX1070 on quite a lot of new AAA games, you need at least an i5 to be able to fully use the GTX1070.
 

JCLDJB

Commendable
May 24, 2016
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Your question is not specific, so I can provide a not-so-specific response which I hope helps.

If you were to have a game that had en equal CPU/GPU usage, then the i3 will reach 100% before the GPU does.

So, yes, your PC will be bottlenecked by the CPU; however as others have mentioned, depending on the game(s) played, and the settings chosen, you can tweak the game settings/graphics settings/resolution to ensure you have equal usage between the CPU/GPU.

I would recommend minimum an i5 Quad Core with a mid-level GPU, such as the 1070 or above.

Still, it isn't a 'bad' set-up per say, and you will not be disappointed with performance, but you will need to upgrade the CPU before needing to upgrade the GPU, hence a more accurate response to your question (I hope) :)

For 4k gaming, you want to go for an i5 minimum, but be prepared to reduce your graphical settings quite a bit (even with a 1070 GPU) compare to HD or 1440p...