Nope - I had 5 seasons at Haverfordwest on FM22. Was never able to get past TNS or Connah's Quay. Was able to consistently finish 3rd, but that was the limit.
TNS and Connah's Quay have a massive advantage as the only fully Professional teams in the league. Trying to topple Professional clubs as a Semi-Pro outfit is always going to be a tall order. Add into that TNS get Champions League money, which is huge in comparison to what other clubs in the Cymru Premier get even if they don't make it past the qualifying rounds, so they always have a significant economical advantage over other clubs which only grows every season.
If you are going to topple TNS though, Connah's Quay are going to be your best shot of doing it.
Edit: I'm wrong, Connah's Quay are also Semi-Pro. I had it in my head they were fully Professional when I played in Wales on FM22, but that could be me misremembering perhaps.
The real mickey take of the whole thing though is that TNS isn't actually a Welsh club, they're actually based in England. Although I am aware they were originally based in Wales, they just happened to stay within the Welsh system after the move to Oswestry.