There's a place called VJ's Bargain Barn that I pass about once every week or two. It has fiberglass tubs in the yard, so I see how they're made. They are NOT made to float.
Most of them are designed to fit in a tub-sized, walled enclosure. Both ends and the long side that fits against the wall just have lips to caulk to the walls. The front edge comes out and then goes down to the floor. So, you've got three short edges, and one that may hold air, and throw the thing off-balance. IOW, they look monumentally unstable to be on the wrong side of water. I think some also have air vents to help them drain.
They're rectangular on the outside, not what you'd call streamlined. I've paddled canoes that were kind of hard to paddle, and I'm sure they are tons better than a bathtub.
Now, an old-fashioned, claw-foot, free-standing bathtub, maybe. Its sort of like a boat. Kinda-sorta.
But you'd still need an awfully good plug.
I'd say an inner tube would be better. Not good, but more maneuverable. And you wouldn't have to detach it from plumbing.
If you're likely to have water problems like that, you'd best plan ahead.
Sue