Filemaker can do this, but can you use filemaker to do it?
That depends on your expertise and how much time you choose to invest in learning how to use filemaker to build such a database.
You might want to try out a trial download of Filemaker to see if you can get it to work for you.
Yes, it can be done. As a former hotel controller I have been "visualizing" what I would need to make it a reality. I have already created a database for a membership, ie country club which includes the billing aspects. I am working on the rooms side with tracking for future availability and reservations, converting those to "stays" in the hotel.