I've never taken note of how long the training takes, but it seems to be a good month of ingame time to get a guy to 10 in a stat at a rough guess. I'd be prepared to bet it takes longer to go up by 1 the higher the stat already is, but I can't say for sure (that's just how I would've coded it).
And no, robots can't stat train like that. They don't even take Recreational assignments unless I'm mistaken.
However, there's this little mod:
Makes automatron modifications affect their SPECIAL stats for Sim Settlements 2 plots.
www.nexusmods.com
Changes some of the parts to have SPECIAL stat bonuses, so you can craft them yourself to be specialists in tasks. It might require taking perks you otherwise wouldn't, but I can confirm that you can get a guy to 25+ in STR or END if you gear them right.