It probably will work with your current PSU, but I would not reccomend it, given my past experiences with older CX series PSUs failing.
I have a system with an FX8350, 16gb ram, and an XFX RX570 4gb. It is alright for most games, but it really is not ideal. Trying to play beamng with traffic uses more than 4 cores, causing the cores to have to share fpu at that point and cripples performance, or so I understand. Like 40fps with a ton of drops making it not enjoyable. Some games perform decently well, actually including beamng if you use some lesser demanding maps with a single core, but some cases I will be held back by the CPU.
Given your 6300 is even less powerful than an 8350, the cases where you are CPU bound with an RX570 would be more commonplace.
I would sell your current pc and buy something more modern, or throw in a placeholder GPU like a 1050ti and use the PC until you can save up for a newer pc.