Will an i3 3240 3.4GHz bottleneck an Sapphire RX 560 4GB

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It shouldn't bottleneck the RX 560 at all. The i3 3240 with the RX 560 should be a fairly balanced system. I'd worry more about bottlenecking the CPU than the video card. The CPU should allow the graphics to reach its full potential up to about the RX 570 level of card. You might experience slight bottlenecking on something like a GTX 1060 6 GB.
It shouldn't bottleneck the RX 560 at all. The i3 3240 with the RX 560 should be a fairly balanced system. I'd worry more about bottlenecking the CPU than the video card. The CPU should allow the graphics to reach its full potential up to about the RX 570 level of card. You might experience slight bottlenecking on something like a GTX 1060 6 GB.
 
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