Tim,No. The license is for the Finale program & registered serial number, not each individual update. For you to become a legally registered owner of the program, the person you are buying from would have to turn over all of his/her rights to you, including the newest version that they have. In other words, there can be only one registered and legal owner for each serial number.
You may want to consider one Coda's lower end products like PrintMusic or Finale Allegro if you can't afford Finale right now. I bought PrintMusic to be used on my laptop and have had great luck with it. Although it lacks some of the features of Finale, I have scored full band arrangements on it that look OK. If you later decide that you really need Finale, Coda has a pretty good upgrade path from both PrintMusic and Allegro to Finale, plus all of your PrintMusic files will transfer to Finale with no problems. PrintMusic an be purchased for about $70(US funds) or less from resellers.
Good luck.
Jim Coull