I just want to make sure this wont hurt anything.
Right before I bought this house, it got a new AC and furnace but they did not replace much of the duct work. This vent is right above the AC unit and is the first vent the cold air passes. It was bleeding cold air into the basement so I covered it.
Best Answer
Whether you tape it or otherwise block it, the effect will be the same and it will not cause any damage to your system; it would be no different than if there was a standard register there that was closed.
The only thing I'll note is that duct tape will eventually dry up and fall off. Ideally you would use foil HVAC tape
(source: homedepot.ca)
Unlike duct tape, this will not dry up and will hold the seal.