The note does clarify your intentions, in that you let her know you don't want anything beyond the mutually beneficial sexual experience. However that might turn her off, especially if she was hoping for more than sex. Hence all the guys' advice to just be light-hearted about the whole thing, hang out, and see where it goes.
If she is already very attracted to you, and does just want sex, sending a note won't kill it, in terms of wordy-ness. She most likely would appreciate that you took the time to express yourself, but then, there are other equally effective ways to express yourself as Syrvin suggested.
Think of how this experience may impact her as well as yourself. You seem like a good guy, and a considerate person
Best of luck whatever you decide.