No, 3770k isn't going to be a very good processor in 2020 and could likely end up a dog gaming cpu by 2021-22. Good cpus are cheap right now with AMD reasserting itself in the marketplace. The Ryzen R5 3600 / 3600x are seriously great 6C/12T cpus for around $200. Here is how it measures up in one of the most cpu heavy games of the generation, where the benchmark was done at 720p with an RTX 2080 Ti to force it to be a straight up cpu test:
Note this is only in one game, as games with less parallelization the i5-9600k and even i5-8400 can pull even and slightly beat the R5 3600. But with 8C/16T being the norm for the consoles next gen it's not a bad bet that we'll get more games coded like AC Odyssey.
The AMD chips are no ing joke this time around. Not like back in the FX days where they were crap. Also RAM is back to being decently priced, so this is actually a pretty good time to do a platform upgrade (eg board + cpu + RAM).
Though I'd probably go with the $310 Ryzen 7 3700X since it's an 8C/16T cpu that will probably last you the entire next console generation.