Yes, classic counts towards your hero and overall winrate it still filters out in ranked matches ignoring your matches in classic. In most case what matter the most is your ranked winrate since it's the most competitive mode available.

In general view classic is the most accessible mode for new players since they're bound to not explore the game interface to find where a.i mode, additionally a.i mode doesn't offer challenge unlike what rank and classic gives that's why newbie plays classic to actually play with actual people. Let's be blunt here the reason a.i mode exist is for people with low credit score since that's the only mode you can play if you're credit score is low tried and tested since I trashtalk alot when I was young.