Historically the free night didn't count or wasn't supposed to at least with Hyatt.com 3rd or 4th night free etc
when booked on Hyatt.com
Even when brought up to the former Gold Passport folks that was the intention.
Having said that there are data points from others through the years when it accidentally did count.
So as long as you don't expect it YMMV if you get lucky.My own experience it did not count.

And now we have rates at Rio for 100 dollars a night with no stay tier credit or points courtesy of the dodgy RIO folks
Why bother? for a cheap room and a mediocre chain restaurant breakfast some of it vile some of it just ok?
I do see where staying here makes great economic sense on a shoestring budget
Just not for me.