Yes, you do! You're status level affords you all the benefits regardless of how you "pay" for your stay. In order to try and maximize the chance of an upgrade, when you book your reservation (I always call the Platinum Reservation Line...such nice, friendly service!) mention to them that you would like an upgrade if possible. They will note this in your reservation notes to the hotel and, hopefully, they will be able to look out for you as your check-in date comes near. Worked for me so far! Cheers!
I rarely get upgrades when staying on points. Others here have told me in the past that I have to be more aggressive, but even that hasn't worked for me. I also started calling the Plat reservation line, requesting that an upgrade be placed on the record, and that hasn't worked either. In my experience, it's hit or miss. Mostly miss.
When you book a reservation online, request a Platinum upgrade in the "remarks" box. Note that finding the "remarks" box is a small trick --- once you select a room rate, back up one screen to find the "remarks" box. When the local hotel blocks (assigns) rooms for the day and when you check in, your "remark" will show up on the clerk's computer screen highlighting your request. Remember, however, that an "upgrade" does not necessarily mean that you will be assigned a suite. "Upgrade" in the elite terms and conditions means "best available room" at time of check-in. And, "best available room" can mean many things besides a suite ---- such as a room with a better view, a room with more amenities (such as a whirlpool tub or an additional bed), a corner room, a room on the concierge floor, a substantially larger room, etc., etc.
All the above answers I have experienced at one time or another. When the upgrade is important such as anniversary or family trips I have found it helpful to call ahead directly to the hotel and discuss what you would like to make you stay memorable with the assistant GM or at least the Desk Manager. I have found they can usually make things happen provided the hotel is not at capacity with other platinum plus travelers when you are planning to arrive. For example when a large convention or peak holidays are involved.