Whenever I've tried the Soldier class, I've either had someone behind me try to run through me that just couldn't which ends up with me being dead, or it ends up with people wondering what the hell I'm skulking around the bases for instead of being in the front line of battle and they'll shoot me. People won't be suspicious of you being a pyro, engineer, medic or sniper as long as you alternate your disguises, be where you're supposed to be and kill what you want to kill before getting the hell out.

I do agree about running backwards though, it makes it look authentic, aslong as you're certain there's no one you might risk bumping into. The number one priority as a spy is to avoid detection at all costs.