Will it work? Yes.
Should you use it? no.
It will work, if sealed well enough, and the seal is maintained regularly, but in the end, it will be a lot less expensive, and a lot less effort to just use good quality plywood.
(Heavy cardboard could be used too, if it is sealed perfectly. One little scratch though, and its finished).
Plywood also must be sealed, but in the event some moisture does make its way in, it won't require removing and replacing the flooring like OSB will. Plywood can withstand several major wettings before delamination causes any real concern.
One major wetting and OSB is done.
OSB was designed to be an inexpensive plywood/sheathing option for areas that are NOT exposed.
In areas that it is NOT exposed, it does a good job, not as good as plywood, but not bad.
Roof sheathing covered by shingles, flooring covered by other flooring, etc.
In the rental communities I look after, we have banned OSB for ANY exposed application. Most have been as shed siding.
Over the years, we've watched people paint, and paint, and paint some more to "protect" the OSB.
It still swells, separates, and rots.
No disrespect meant, use OSB if you wish, but if you can't afford to pay the difference between OSB and plywood, I would question the economic sense of building a teardrop in the first place?
Please don't take that statement as offense, for it is not meant to be.
It wouldn't make sense to buy a car if you couldn't afford the gas to operate it?
There is NOTHING wrong with building an inexpensive trailer.
Many of us have taken on the challenge to see how little we can spend, and some pretty neat examples have been the result.
However, it is important to understand the difference between saving money by using donated and low priced quality materials, and using cheap, low quality materials!
If you're on a tight budget, consider used materials.
Consider asking friends, family, co workers if they have some extra unused building material taking up space in their garage, basement, etc.
Once they hear about your cool project, you may have more material than you need...
Good luck with your build!
Check Craigs list, the local paper, recycling organizations, etc.
Good high quality building materials CAN be had for next to nothing if you just look for them!
Rob