Certainly it must have, more than that, it helps widening the definition of habitability as slightly too cold planet must be still habitable further out to the sunny side, and slight too hot one must still be habitable deeper into the twilight zone.

Anyway if the water is not all locked up in ice on the dark side. There could be so damn much water that enough sublimates to rain on the hot side or the terminator.

Still, not a place I would start looking for life.