Is the Shaw Rigid Core HD Plus vinyl plank acceptable for use over tile in a 3 season sunroom (drywalled and has windows, but no HVAC)? Also, I have ecosilent underlayment I plan to put down underneath it.

Yes, Shaw Heritage Oak Rigid Core HD Plus can be used in a 3 season application. The floor has underlayment already attached, so we really don't recommend using any additional underlayment. However, it is allowed, as long as the second underlayment is a maximum of 3 mm thick and has a minimum density of 11.7 lb/ft3.