Certainly some teams would have an advantage, but unless they were the "dream team" for a player I tend to think the player would follow the money. Heck, let's say the Yankees offered someone 1M instead of the Astros at 1.4M - chances are that the guy is traded before making it to the Bronx anyhow (possibly to the Astros). Also, a prospect may have a better chance of making it to the big leagues faster on a team where there's better chance of a vacancy existing. The problem of some teams having the advantage is certainly the counterpoint to this kind of system though.
Maybe give all teams a weighted draft cap bonus based on lack of playoff appearances over the last 10 years or something, along with a bonus for extending their own players into FA years or losing a prime player to FA.