No, beyond the possibility the first property would think you have left and check you out. Leave items in the room, put out the Do Not Disturb sign, decline housekeeping, have the record noted you want the room the entire time, leave a sign, something. It still might happen, but you can shrink the possibility.

You are very unlikely to get stay credit for both rooms. IT is supposed to catch that and usually does.

(Can create an IT hiccup. Keep the paper folios till you verify enough nights of stay credit and points have posted).