No. New Jersey's residential building subcode keeps plumbing, mechanical equipment, ducts and dryer vents out of the cavity of the common wall shared between two townhouse units. That wall is the fire separation between one home and the next, built to stay solid and continuous from the foundation up to the underside of the roof sheathing, and a duct or vent routed through its cavity would open a gap in that separation at exactly the point where it has to hold. A good share of the homes in Gloucester Township and in Voorhees are townhouses or other attached units, so this question comes up on plenty of renovation and new-installation jobs in both towns, not just once in a while.
What the common wall is built to do
A party wall between townhouse units is rated to resist fire for a set stretch of time, long enough for the units on either side to be treated as separate buildings for life-safety purposes even though they share a structure. That rating depends on the wall staying unbroken, the same layers of framing, fire-rated board and any fill running floor to roof without a gap cut through it for a duct, a vent, a pipe or a run of cable. Every penetration through that assembly has to be sealed and fire-stopped to keep the rating intact, and a duct or vent chase is a penetration the code does not want in that wall at all, sealed or not, because the opening itself works against what the wall is there to do.
Jobs that tempt a crew toward that wall
A few projects run into this more than others. Adding a bath or a laundry room on an interior wall sometimes leaves a plumbing or dryer vent route that looks shorter if it borrows the party wall rather than turning a corner into the unit's own framing. A new return for an upstairs hall can look like it wants the same shortcut, especially in a townhouse where the stud bay along the shared wall is the only open run nearby. Dryer Vent Installation is where this shows up most, since a straight shot through the party wall toward the back of the next unit can look like the fastest path to the exterior. The code does not treat any of these as exceptions. The wall stays closed whether the run is supply duct, return duct, a dryer vent or a drain line.
Where a townhouse unit can still route a duct or a vent
Every attached unit keeps a full set of routes that belong to it alone. The front and rear exterior walls are available for chases and vent terminations, since those walls face the street or the yard rather than the neighbor. Floor joist bays running from front to back or side to side within the unit's own footprint carry duct and vent runs the way they would in a detached house, as long as the bay does not cross into the shared wall assembly. Soffits built along an interior wall that is not the party wall give a boxed-in path for a return or a supply run without touching structure that is rated for separation. The unit's own share of the attic, where the roof framing sits entirely within that unit's footprint, is usually the most direct path for a dryer vent or exhaust duct headed up and out through the roof rather than across the shared wall toward a neighbor's exterior. Air Duct Installation planned around these routes from the start avoids a rework later, and in most of these townhouse layouts there is more usable chase space along the front, rear and interior partitions than the party wall would have offered.
What to do if a run already lives inside the party wall
Older work sometimes turns up a duct or a dryer vent already routed through the common wall, usually from a renovation done before anyone checked the assembly it was passing through. An opening up of a wall for Air Duct Repair or a dryer vent replacement is the point where that gets caught, since it is the first time anyone looks inside that cavity in years. The fix is a reroute into the unit's own framing rather than a patch that leaves the duct where it is, because sealing around a penetration in that wall does not restore the fire separation the way removing the penetration does. A technician who finds this mid-job will flag it before closing the wall back up, since covering it over without correcting the route just hides the problem for the next person who opens that wall.
Permits and the association before anything changes outside
A new duct run, a relocated dryer vent termination or any change to an exterior wall or roof penetration goes through the township's permit process before work starts, and Gloucester Township and Voorhees both review that kind of work the way any other municipality in Camden or Burlington County does. In a townhouse with a homeowners association, the exterior face of the building, including where a dryer vent cap or an exhaust termination sits on the siding or the roof, is often covered by the association's own rules on top of the township permit, so a written estimate for this kind of job should spell out which approvals the homeowner needs to gather before the crew shows up to cut an opening. None of that changes where the duct or vent is allowed to run. It just adds steps before the work on the unit's own exterior wall or roof can begin.