No, there's not a way of measuring it on an assembled bike. (On a bare BB shell, one could hypothesize some ways of measuring the parallelism, but it's not something anyone really does.)
In an extreme example you would find it was impossible to adjust correctly for adjustable preload types such as Shimano, or was tight and didn't turn freely in automatic (wavy washer or elastomer) preload systems.
Usually it's more subtle than that though, with the only real diagnostic method being, "Gee, for some reason this isn't spinning as freely as it should, let's face it to eliminate that factor." Or it's suspected someone is wearing out BBs seemingly prematurely, especially if a fresh one seems to not spin well.
Just pre-emptively facing and chasing the BB is really the way to go. That's the only way to actually know it's right.