Yes it makes perfect sense. I would generally prefer using the boost/stdlib functions where possible rather than their Qt alternatives.
It makes the code easier to port to the next framework.
It makes is easier for new non-Qt programmers to get upto speed.
Boost has some great functionality and is getting more all the time.
note: strings to/from widgets are probably the main exception – inside the GUI I would use Qt strings to save confusing casts everywhere.