Sometimes, but most often it's just that the heavy doesn't react fast enough.
And who do you prefer to disguise as when playing spy? I often use demoman because he's a pretty basic class but not too slow.
Scout: Horrible choice, anyone can see that you are moving too slowly to be a real scout
Soldier: Mediocre choice, good it some situations where the enemy is bunched close together because of slow move speed
Pyro: Mediocre choice, it will become apparent that you are a spy when you dont try to light anyone up.
Demoman: Great choice, spy can act like he has a stickybomb trap and is waiting as well as good move speed.
Heavy: Poor choice, moves very slowly and most people will become suspicious of a heavy not getting any kills.
Engineer: Mediocre choice, good in some situations where three or more sentry nests overlap.
Medic: Horrible choice, you will be found out the second anyone calls for medic.
Sniper: Great choice, spy can act like he is strafing for a headshot.
Spy: Mediocre choice, good move speed but most people will spycheck more often if they are reminded of spies.