Many including me have done this for years with parts cars. Just make sure you have a very good bill of sale AND keep the title handy.
Works best with out of state cars since VA DMV wants to know about sales in state for that reason.
Since the seller is expected to fill out the owners card with the buyers info and send it in, you could always put an out of state address on it. Not sending the card in often doesn't work as the VA DMV is relucktant to remove car from PO's info without new owners info. Realistically most people quickly forget who they sold the car to and lose any paperwork but you could buy something from someone like you
Might also check the DMVr web site about "parts cars."