Would squirrels use a house I bought if just put on my balcony floor?

Hello Edward, squirrels build their own dreys up in the trees where there's a fork in the branch which are made from a mix of twigs, grass, fresh and dried leaves although they occasionally will use roof voids if they can get access which results in major nuisance factor necessitating their removal to prevent damage; they do not use boxes so would not use a "house". I would discourage them from getting too close to your building and try feed them in the garden somewhere; or if you are in an apartment and have a communal garden where you could place a nut feeder for them. Having said that if you are in an apartment other residents may be against you feeding grey squirrels. Hope you can continue to enjoy watching your squirrel enjoy the nuts but don't worry about a roost or nest for them as they would build their own drey.