There are a number of issues that a local building code officer may question. Fire can pass from floor to floor and room to room through the openings in ductwork. Radon can pass from the openings in the basement to the rest of the house. Local code may have some statements about these.
Other issues are about where the air is coming from to replace the air sent to the basement without a return. It may be coming in the crackage around doors and windows upstairs increasing discomfort in upstairs rooms from cold air drafts and raising the fuel bill. Allowing more heated air to enter the basement will take it away from the upstairs. As many installations are guesses by untrained installers, the heating unit may be far larger than necessary, so the heater might be large enough. If the heater is the right size now, then adding heat to the basement will increase the needed furnace size by another 50%.
As the basement is masonry, particles of cement, silacates and dust float in the air. If when you walk in the basement a slight cement taste appears, this dust can circulate up to the house from the furnace blower. Floating silicates produce respiratory problems such as sarcoidosius over time. As the basement walls are cinder block, they are porous, letting outdoor air and ground moisture pass through and the pores present a place for mold to grow, which may be spread throughout the duct system. Sealing and insulating the walls may reduce the problem and will also save on the increased heating bill.
If you can eliminate all the above problems, you can do as you wish without guessing.