Should be just fine.
The different gaps are not between the teeth, but between the chainrings. The chainring spacing from 9-10 isn't a big deal. It's when you are using a 6-7-8 speed crank on 9-10-11 speed chains. The wider gap between lower speed crank chainrings allows the narrower chain to fall between the rings rather than landing on the next ring.
BB maybe different, but as you said you plan to replace that anyway.