If there's electric there it can operate a fan and a light easily. The light kits are meant to work with the fans, so that the wiring passes through the fan to the light to be connected. It DOES look like there's probably a fan box behind that plate (why else would you put a plate there instead of just finishing the ceiling???), but as others have noted, you won't know for sure until you open it up and look. Good luck!

Have you looked in to universal remotes for ceiling fan and light? Ask at your local lighting shop. https://www.amazon.com/Universal-Ceiling-Fan-Remote-Control/dp/B00A2WU4CK

I’m having a very difficult time getting my question across - I’m looking for advice on a chandelier ceiling fan & yesterday on houzz I was reading an article on ionizing ceiling fans but I’m notable to tell if they produce enough circulation for a large master bedroom. (Fingers crossed this gets read)

If you'll look at the power supply fan on the back of a desktop computer, you'll see what's wrong here. The blades are surrounded by a round hole in the fan body, just slightly larger than the blade diameter. They're made this way because a fan that's trying to "pump" or mov air from one area to another works best when it's surrounded by a baffle. Well, your tray ceiling is acting as a loose baffle. The fan tries to pump air from above, but it's mainly pulling air from (effectively) a closed box. That's why it moves less air than it should - there just isn't much in that little box behind it. So, the solution is to lower the fan until you get the breeze you're seeking.