There is no need to have a vent BEFORE the trap.
There is only one reason I can think of installing a vent BEFORE a trap, and thats if some moron put a easy trap on a unit that is interally trapped.
IE: Climate master geothermal heat pumps are internally trapped. If an inspector can't get it through his head that the unit is trapped internally, and makes you install an external trap, then you would need a vent before the SECOND trap.
Having 2 traps in a drain line will create an air lock. This is why plumbing has a vent pipe.
If we are talking about a vent AFTER the trap, we're in a different ball game. Everytime I do an install with a drainline that goes from one floor to the next, and goes only knows what moron ran it, I'll install a vent AFTER the trap. This will prevent the airlock. I'll make sure the top of the vent is higher than the coil pan, or is within the secondary pan.
The downside to installing a vent BEFORE the trap, on a standard gas furnace/ac installation, is that your dumping cold and hot air into the furnace room. Doesn't sound that bad, but your customer WILL complain about it.
If you install a vent before the trap on a air handler, your now allowing the air handler to suck water back into the coil. It won't drain.