Personal experience is that it doesn't really matter how you paid. Booking via Prive/Globalist/Guest of Honor matters more than whether you paid with CC/points.

My recommendation is that if a suite/better room/ is important or desirable for you on a specific stay, reach out to the hotel in advance (email to the GM or call the front desk at the beginning of the day before check-in) to say what it is you would like. Be gracious and willing to accept "no", but saying things like "I'm traveling with family and it looks like suite ABC is available for my stay and I would really appreciate the extra space as we stay at your hotel to vacation. If you could provide an upgrade to that room that would be fantastic. Thanks!". If you don't get it in advance, just mention the same thing at check-in. Between the two as a globalist I've been able to get a suite (or nicer room/suite) when it was important to me most of the time. Obviously, I apply a TSU when available as well, but that's not always an option.

If you don't have globalist status, I would highly recommend booking with points through a friend with globalist or booking with Prive using $$ using a travel agent.