A couple years ago I had seen a few reviews of the weaker Pentium g4560 being paired with a GTX 1070, 6gb GTX 1060, RX 580, 3gb GTX 1060, and the RX 570. The poor Pentium was bottlenecked in games which used more than 4 threads, but despite the bottleneck the Pentium still scaled well with the 6gb GTX 1060 and below. The RX 570 and GTX 1050ti seemed to run fine with the Pentium. The Pentium g4560 had trouble keeping up the the GTX 1070.
The GTX 970 is about equivalent to the 3gb GTX 1060.
The Ryzen 3 1200 has 4 full fledged cores, whereas the Pentium g4560 is a dual-core with Hyperthreading, so the Ryzen 3 1200 is a better CPU for gaming. The Pentium might have better single threaded performance but it's not that much better, and it's hard for the Pentium to run at it's maximum single threaded potential when the CPU is maxed out. Hyptherthreading results in 2 threads sharing the resources of a single core.
The GTX 970 is a good pair with the Ryzen 3 1200 but IMHO the 8gb RX 580 would be a better card to combine with the Ryzen 3 1200.