When you run for president, someone will drag up the fact that you paid for a hotel room, in cash, incognito, for some woman and wonder why. It will be spun into something perverted.
Almost kidding by the way
Just know that the homeless out there do know where to go to get shelter and food. She may enjoy a hot bath and a room for the night, may very well forget it in the morning, and the only thing gained is the feeling that you did something well. But did it do anything good?
Living on the street and knowing you are there, after a while one would get accustomed to it and adapt your life until something substantial changes it. Does it do harm to hand out a night of relevant luxury only to be returned and Reminded of your condition the next day? Change her life dramatically or walk away, but don't tease. Spend the value of the night on a donation directly to the food closet and feed 20 people for the waste of 1 night's luxury.
Before someone balks at my ignorance of the homeless lifestyle, understand that I have been part of a food closet program to help out locals for nearly 18 years now. I know how much food that 1 room can buy. If you want to do some good, Really do something that counts.
IMHO of course. *EDIT* Not your house though, really, don't go there. Your family is exposed to things you are not considering, Never that.