I don't think it's necessary. I have invoiced without an address before. I just emailed the person and put their email address and phone number in the area where I normally put an address. But that was just a $25 invoice...
I think the real benefit of having an address is it will make it much easier to go after someone in court if they don't pay you.
I would just ask "what do you use as your address." It doesn't seem insensitive to me at all, but maybe I'm clueless. But - if they do banking, go to the Dr., Drive a car, receive mail of any kind, they must have an address. Maybe it's a PO box or a friend's house. I would think it would be the address where their boat is, slip number X. (Unless maybe they're traveling around the world in their boat)
Then I would either hand deliver or email the invoice, especially if you sense they don't check mail much.