It is OK but there might be some problems. If the paint is solvent based then it could react with and possibly dissolve the original paint causing bubbling and possible loss of adhesion. Plus the smell could be a major problem.

Make sure the marine paint doesn't require a special primer.

If you need a tough paint why not try a water-based epoxy? Very tough and fairly easy to apply.

Thank you for the previous answer. The room is in an old 1954 New England Cape so the finish walls have been plastered. If the walls beneath the vinyl panels in the shower stall are in good condition I will only replace the outside the stall with Blue board and paint all the walls with Marine paint until I can do the renovation correctly. In your opinion is this OK to do? And How long will the fumes from the marine or epoxy paint last?

This will be fine and should last for a long time. The smell depends on the solvents in the paint. Read the label for the marine paint, it will list the clean-up solvent needed and this will tell you if it is water based or solvent based. The water based epoxy has a little smell but no where near as bad as a solvent based paint. All paints and coatings take a while to cure and during this time they will give off VOCs. Plan on not using the bathroom for a few days during this process.

Solvent smells can linger for a few days so aggressive ventilation is a must.

Personally, I would use a good water based epoxy. Plan on 2 coats over a good primer. My favorite is Pittsburgh Aquapon, easy to use and a 1-1 mixing ratio with no sweat time needed. If this isn't available in your area visit your local paint store, a real paint store not Home Depot, and see what they have.