Can I vent a portable air conditioner unit through a heat vent?
You will be pushing humid warm air into the ductwork. That is not a good plan for a number of reasons.

1) This is essentially the same as venting the portable ac into the house since the ductwork feeds air to the house. The ac unit is trying to remove heat and humidity from the house to cool it. That is why the vent needs to exit the living space.

2) introducing moisture into the ductwork  will cause mold to grow  in them and may cause them to rust if they are metallic.

3) The humid air pushed into the duct work will find its way to the expensive parts in your furnace and damage them as well.

I would try thinking of it like a clothes dryer that you need to vent to the outside of your space. Could you add a duct through a wall with a weather cap on the outside termination?