Yes, Flatbed was built around the Can-Dive Deep Rover submersible. The Cabs were built around another type of submersible from Canada. There was also a full size dummy Cab Three for crashing around the Moon Pool set. When the movie was finished the submersibles were stripped back to their original configurations and returned to their owners.
There were two 1/8 scale Flatbed models and three Cab models originally built for the movie. One of the Flatbed models was destroyed, intentionally and on film, for Lt. Coffey's demise when it imploded. The other Flatbed is in the hands of a private collector. I think Cab One was given to Jim Cameron and the hero Cab Three was wrecked for some post Deepcore crash shots.
We also built a 1/14 scale model of Flatbed, I have no idea what happened to it, and another model shop built radio controlled wet for wet 1/4 scale Flatbed and Cab models for the chase sequence.
An update - Jim Cameron has the 1/14 scale Flatbed but it was badly damaged when it took a dive off a shelf. It's being restored now.