I am going to tear out the old baseboards before installing my new hardwood floors. My plan is to use new baseboards to cover the expansion space after the floor is installed - instead of installing the new baseboards, installing the hardwood and then using 3/4 round to cover the expansion space. Is there any reason that this wouldn't work? It will be a floating install of engineered flooring.

Your plan will work just fine. It is done all the time and a good solution for those wishing to replace their existing baseboards. For those with tall and good quality baseboards, it is more effective to use baseshoe than removing (and risk breaking) the existing baseboards. But if you're replacing cheap, builder grade base, yes, the way you're describing it is the way to go.

I'm replacing my baseboards, and prefer the "shoeless" look, so will not be adding any shoe molding.