If you are using two different airlines they could care less and you should have no problem checking your luggage all the way through. If it is the same airline at your transfer point, you could get some anal person who could give you problems but this is highly unlikely as the airline would have difficulty proving what your true intentions were.

The biggest problem with two different tickets is the airline will not protect you on a later flight if you miss your connection and you could end up with paying much more than what your savings were.