This could be an option, as long as a few conditions are met.

There should be a damper

A damper will prevent outside air from entering the exhaust pipe, traveling down the length and entering the conditioned space. Most exhaust vent covers are designed in such a way, so that even on windy days the exhaust can still be exhausted. If you just have a pipe pointing to the outside, it's possible the outside air pressure can overcome the exhaust air pressure preventing the exhaust from exhausting.

There shouldn't be a way for the exhaust to reenter the building

If you simply close the window on a pipe that does not completely fill the opening, it's very likely that air pressure differences will force the exhausted air right back in the window. You'll want to devise a way to prevent the exhausted air from reentering the building. This other answer illustrates a way to install the vent, while blocking the entire window opening.

If you have a vapor barrier (e.g. sheet polyethylene) behind the drywall, then you have a major problem. Painted drywall is airtight but not vapor-tight; moisture can migrate through it. And when moisture migrates through the drywall and hits the polyethylene sheeting, it has nowhere else to go. The fact that it currently condenses on the walls tells me that the walls are cold. That means the polyethylene behind it is cold, too. That means water vapor that gets through the drywall will inevitably condense on it and drop to the bottom of the wall, eventually rotting the whole thing out from the inside. Not good. Mold will probably not develop on the drywall at the top of the wall because that's not where the water will be collecting; it's the bottom of the wall you should inspect.

Vapor barriers in walls are generally a bad idea, but if there is any place you could safely have one in a bathroom like this, it would be on the inside, in the form of a water- and vapor-right waterproofing membrane, like RedGard.

If you are unwilling to rip out this assembly and redo it properly (with Redgard-coated cementboard instead of drywall, and no plastic vapor barrier inside the wall), then I would highly recommend preventing moisture build-up in the bathroom in order to preserve the integrity of the structure.