Average accuracy

No and it wouldn't be a good indicator of skill either because tactically rich positions are always gonna give you lower accuracy then simple trade down to endgame positions

Any stats kept for players average accuracy #?
For individual accounts, yes
Under the stats page for each pool that is tracked, you can see the average accuracy of all games you have analyzed.
Insights also has an average accuracy for each pool it coveres, over each selected time period.
Any stats kept for players average accuracy #?