Does a Sump Pump Have to be Vented?

I am in the process of finishing my basement.  I have a sump pump in
one corner with a discharge pipe (going to the storm drain).  There is
also a vent pipe which is simply a run of open PVC going from the sump
pit to the outside.  If I put my hand over the vent pipe, there is
positive pressure (i.e., cold air is coming in from outside).

The sump pump pit will actually be on the inside of a finished room
with a removable platform over the top (serving as an end table). 
[Note: This has already passed inspection].

I noticed today, that the vent pipe is very wet as the humid air
condenses on the pipe.  This is a problem as this pipe is about to be
closed up behind drywall.

Is a vent pipe typically required for a sump pump?  If so, what is the
best way to control the condensation problem?

I know I need to check my local building codes, but I am interested in
any preliminary comments or recommendations.

Thanks