It would be a literal waste of money, in my opinion.
At least with the G4560 he's on the correct socket and RAM type for direct upgrade paths, for effectively the same price and more single threaded performance..
That's why a Ryzen 4c might make sense.. But honestly, i'm an AMD guy, I like AMD chips, but noone should really be buying anything built on the Steamroller architecture.
From what i've seen the AMD A12 9800 Ryzen based APU might be good for budget gaming, competing at console speeds but I don't know the prices or how it would perform in comparison.