It appears that the air conditioner condensation drain pipe maybe improperly connected to the vent pipe in the attic. The biggest concern is sewer gases entering the living spaces.
In your case, the condensation drain pipe is installed properly and leads to the outside. However someone decided to disconnect this pipe and cap it of. Next a condensation removal pump was installed and the hose terminates into the vent pipe.
This is a first for me and conversations at many forums gives different feedback. The primary concern is sewer gases entering the living space of your home. Therefore, some says it is a no-no to tie into the vent pipe, others claim it is an ok practice as long as there are p-traps involved.
I do not know the ramifications of sewer gases traveling through the condensation removal pump especially during the winter when the heat is on and the condensation hose drys out. Therefore, my best recommendation would be to have the condensation drain pipe reattached making sure there is no blockage that caused a repair using the pump. Using gravity uses no electricity by the way.
The next concern is the secondary drainage system. The drip pan is open to the attic. If the condensation removal pump fails and water backs up in the unit the drip pan could over flow before you could figure out there was an issue. We recommend further evaluation from a licensed plumber.
Guys what do you think?