How annoying, I suppose, would depend on how far back they go. As has been said by people far more articulate than me; it makes no sense to modern eyes that Lois could be around both Clark and Superman that much and not put two and two together in short order. And then, it makes just as little sense that Clark wouldn't realize that Lois wouldn't put it together eventually. Hell, you could swap Lois for Jimmy with equal validity (he isn't stupid). I don't know if Perry White has been around Superman enough to make the same type connections.

TL;DR: This only works if it's short term. The classic love triangle just wouldn't work these days.