There are products on the market that are supposed to take care of that problem. I believe air conditioning places carry it or can advise where to purchase it.
It is called condenser cleaner and many servicing agencies use it.Spray it on and all the gook falls to the bottom and somehow disappears .You can remove the blower motor or use the long tube to get in there. Depending on where you drill a hole for the straw may work ,don't know. Suggest to stay away from evap core when drilling because that can be a very expensive cleaning !!!!

 

I agree with hanky, If you spray something like simple green or a cleaner into the air opening on the outside of the lower windshield cawel ( just below the wipers) you can get a pretty good cleaning that way but what makes you think that there is a problem anyway ???

 

F150-07-4.6 brought up a good question !!

If you are dealing with an odor problem coming from the A/C vents , you might want to check and make sure the Evaporator drain (rubber tube) is not obstructed with debris. If you park under trees a lot the beautiful falling leaves small pieces drop down in the fresh air intake and begin to get musty and share their fragrance with the occupants in the vehicle.
Not sure if your vehicle has a "Cabin Air Filter" which if it does, may be part of the problem.