Jennifer, personally I wouldn't if you were going to try and seal it into the drain, too. I think you'd be more likely to have leak problems doing that. But, what you could do if you have access to the trap area below the shower and between floors is to create an evaporation pan that sits in the joist space directly under the drain flange and trap by stapling a sturdy plastic draping to the joist sides, bringing the ends up, too, so that any minor leaks will be contained in your "pan" and evaporate without damaging things. If you're putting in a vinyl flooring before a new shower, I like to run the vinyl continuous under the shower area, too, and leave the vinyl about an inch or so too long at the walls so that it rolls up the studs a little and helps direct any water leaking out onto the floor where I can see it. If you're doing tile or something else, you can just vinyl under the shower and get about the same results. This is also a great idea under dishwashers; water will then run out onto the kitchen floor in front of the dishwasher warning you of a problem, rather than finding rotten wood a year later.
Whatever you might put in below your manufactured pan, just be sure the pan has good sound support everywhere it's supposed to, and that in itself will best prevent future drain flange leaks.