If the studwall cavity is uninsulated there are few drying issues, but it's good to keep bathroom air from entering to find colder surface onto which to condense. In most cases it will be generally safe to blow cellulose into those cavities, but more information about the material stackup of the wall, window flashing, etc. is necessary to address that. (A competent insulation contractor would be able to assess the relative risks.)
Moisture never condenses on warm things (pipes, wood, or bricks), only materials colder than the dew point of the proximate air. The dew point of bathroom air peaks pretty high during showers (which is why even the not-so-cold mirror will fog up), but typical heated/conditioned room air will have dew points between 35-40F during the winter, 55-60F during the summer. The mold risk issue is from cold wood sheathing accumulating excessive moisture from air leaks or vapor diffusion from the interior over the winter.
As long as your vent pipe is air-sealed well from the interior where it passes into the studwall portion it won't create a problem. Far more moisture will move through the wall from air leaks than from vapor diffusion alone- vapor barriers aren't needed in an uninsulated home, but air tighness still matters. If there is wood sheathing on the exterior of the studs, with an air gap between any tar-paper (or even bare plank) and the brick it won't need a vapor barrier even after insulating in much of NY state, but it may in the coldest ZIP codes. Again more information is needed to make that call.
Note: Bath exhaust ventilation depressurizes the bathroom relative to the outdoors when running, so during the winter it will be pulling dry wintertime air through minor leak points rather than than driving humid bathroom air into the wall, which is good. In summer it hardly matters, since outdoor air dew points are rarely above the temperature of the indoor surfaces in NY even when it's pretty muggy out.
Plumbing in exterior walls can present a freeze problem in colder climates if there is more insulation between the pipe and the warm interior than there is between the pipe and the cold exterior. Be sure to assess that carefully too before insulating- sometimes it's easier to leave the stud bays with the plumbing uninsulated.