Welcome to Insiders. As to your question, it depends on - just about everything! Seriously, most properties only set aside so many rooms of a certain type (usually the smaller rooms) for booking on points, but here again, from everything I've read on this forum it can depend on a lot of things. Primarily, making exceptions to this somewhat nebulous policy/practice is at the descretion of each property. Another factor is how early you book on points, depending on how popular the property is. From all that I've read of other's experiences here, it just varies from property to property. I would contact the property management or front desk, and see what they can do for you. Sometimes you can book your room on points, and receive a room upgrade, depending on local factors, like how booked the hotel is during your stay. Give them a call and let us know how it goes for you.
Pluto77 is absolutely right--it depends on just about everything. Last Thanksgiving week, we booked for points at the Downtown Greenville SC Courtyard, and they upgraded us to an absolutely beautiful suite. Thanksgiving week wasn't very busy, so I am sure that had something to do with it. As well, the manager and desk staff were very helpful when I called in advance and asked whether they might consider an upgrade if one was available. Couldn't have asked for nicer treatment, a more convenient location, or a nicer property. Highly recommended. Bottom line, advance inquiry and nice manners go a long way.
alanders1, I am a platinum member and stayed at a Residence Inn in Toronto in March. I wanted to book a 2 bedroom with points but couldn't. It wasn't critical b/c I was able to confirm a crib for my toddler and didn't need a 2nd room for her. Upon check-in, I simply politely asked if they could upgrade me to a 2 bdrm and the front desk did so with no hesitation. He said that if they have it available, they will do it. If you really need a 2 bdrm, I would call the hotel now and ask for it. I've found being polite goes a long way!