The drain from the evaporator/heater core box isn't very big, intended to handle condensate from the AC core, only. A little algae or dirt/dust buildup in it can cause it to leak into the passenger floor. The climate control system ductwork mounts up to the underneath of the metal cowling in front of the windshield. It may be that it's been removed at some time and the seal was damaged. Getting it exposed isn't a terribly hard job, but it's a little time consuming.
If you remove the instrument cluster, the vinyl radio surround and the dash, you can see everything. There are only about 8 screws for the cluster, 4 for the shift surround, about 4 for the radio surround, 8 for the 2 front speakers and maybe another 8 for the complete dash. It sounds as if the leak is severe enough that it should be fixed to prevent carpet rot and rusting of the floor area.