Yes, that is the case.
Then you can register it in the 'passenger' class if the pick-up truck does not have any business advertisements and it is used exclusively for non-commercial purposes.
I see.  I happen to also own a van. What if I install seats behind the driver in a van?
In that case you must also install seatbelts that meet NY State Occupant Restraint Law requirements. These modifications must be permanent.