I just returned from Ingapirca. The ticket clerk was unequivocal: reservations are required (link below). If you show up and there is space, then they will let you in of course. But if there are 7 buses of visitors, as there were on a rainy Friday, then you’ll have to wait.
Also, FYI, the road was washed out a few kilometers from the site (on the smaller road), and it was very difficult in a smallish rental car. We almost got stuck in the mud. Thus, I would recommend an alternate route: Tambo on the E35, then Carrera Ingapirca. Much shorter from E35 on an easily passable road.