Do you lose some of the "first win of the day" IP boost by playing in Beginner AI games?
No, the +150 bonus-of-the-day is not impacted by playing an AI game or a Custom Game instead of a PvP game. You need only make sure that you win the game, and you'll earn an un-changed +150 IP on top of however much (reduced) XP/IP you get normally.
It's actually not uncommon that some players will specifically do a relatively quick AI match just to secure that win, especially if you're having a bad day on the PvP end.