I think so. People have certain traits and physical characteristics that when other people observe us, they recognize us by associating those traits that they can identify us with.
Even with a 1 second glance, people who know who you are can recognize us by how we walk, stand, carry our bodies etc. (mannerisms)
Of course, the eyes. when we engage people, we look into their eyes. We all know and understand where this statement is going.
So, like you said, even when we are covered up from head to toe, (para-phrasing) people who are close to us or come in contact with us more than a couple of times, they can recognize us.
Begs the question, When someone commits a crime against someone else when a group of people are around, that no one see's anything.
It depends on how much attention you pay someone. People give off a lot of body signals (they way you walk, your general height and shape, eye shape and colour, the way you use your hands.) So anyone who has paid you any attention is likely to recognise you however you dress.
Some people just pay more attention that others, so they're more likely to recognise others. Women, for example, are more likely to recognise people than men. Men tend to be more oblivious to non-verbal cues.
I generally recognise people by their voices. Not just the tone, but intonation, accent and so on.
I've done quite a bit of theatre, so I've run into this phenomenon before. A friend of mine played Death when we did a production of Terry Pratchett's Mort, and to me he was instantly recognisable. But not so recognisable to others.