I can't think of any reason why not. How old are 9 speed 105s, though? It may be that by the time tiagra got to 9 speed it was just the same as 9 speed 105 anyway. But by all means go for it if you've got a decent source for the 105 kit!
You are right m8, I've just had a look for 105 9 speed kit and its even rarer than Tiagra! Scratch that idea - a used 4500 lever it will need to be.
