When you're able to discern a poplar body's influence on tone, you'll find that it sounds like, well, a poplar body. It'll have rounder, less articulated definition than, say, ash. Does that mean it has crappy tone? Nope. Not if you're looking for that tone. It's like folks who want to know whether a slapped P-Bass will sound OK. The answer is: sure, but it'll sound like a slapped P-Bass and not a slapped J-Bass - and if you're looking for a slapped P-Bass sound, you're golden!
And, BTW, the MIA Musicman S.U.B.s from several years ago have poplar bodies. I'd be hard pressed to think of those bad boys as lacking in any way.