I saw a documentary once where a wasp had a specific routine when arriving back home, and they showed the routine normally several times and then they showed the wasp doing the exact same thing after having been beheaded- no head to clean, but the wasp swiped its foreleg in the general area, then continued on the rest.

This was given as a difference between wasps and humans, or more generally, between instinctual and considered actions.

At first I worried a little, because I noticed how much I did on autopilot. Then I realized how much everyone does on autopilot and then I worried a lot.

I think if we were able to continue walking around without our heads, people absolutely would.