Sure, it's fine, and you can send it to as many schools as you like. There are a ton of threads on this. It's not binding whether or not you promise anything, and it is treated as such (i.e., it doesn't mean anything, with the only exception being later in the cycle when you are on a WL, when it would be assumed that you wouldn't waste your time if you weren't serious, and they will know soon enough if the take you off the WL and you don't CTE immediately).
And even then, they are meaningless! If the application is not otherwise compelling at the school where the stats are high, the school is going to figure there is something wrong with a candidate who is begging (especially at this point in the cycle), and, they'll be correct. If you have been yield protected out, it has already happened, and telling them you have nothing else at this point is going to signal to them that they dodged a bullet, not that there is gem in the bargain bin waiting for them. The opportunity to make this case is in your secondary, not in January when you are feeling nauseous.
The very language that you're using here shows why Admissions Deans treat all of these as lies.
