Per Jack Campin:
"McGrath - there is an obvious difference between the tone of a string ringing its full length from the nut and one that's stopped some way up the neck with a capo. You don't need to be a guitarist to hear it. A capo is effectively a mute."

I'd argue that the truth lays somewhere in-between, but I'm leaning more towards McGrath's opinion. It's true that a capo may partially mute or muffle the fully ringing tone of a completely open string, but not nearly to the extent that a finger does. If nothing else, an un-fingered string ~ whether open all the way to the nut or just to the capoed fret ~ continues to sound between and through chord changes. A string held down by a fingertip is deadened the moment the finger ceases to fully depress it. Depending upon the player's stylistic intentions, and also his/her level of skill, the time that fingered strings remain firmly held and fully heard may be very short indeed.

I am a guitar player, of some 45+ years standing, and while I can't claim always to hear the difference between an instrument with or without a capo, nor ever to hear the key in which a piece is being played, I can very often hear the chord shapes being used for a given piece.

That is, I can often recognize the set of key-of-C guitar chords, even though I cannot be sure of the absolute pitch. The instrument may or may not be in correct tune, and may or may not be capoed at the first or second fret*, but I can recognize the C/F/G chords by their voicings/inversions, by the bass runs available to the player, and, yes, by the combination of fingered and open strings in each chord.

*If the capo is WAY up the neck, yes, of course, I can recognize that the overall pitch of the instrument is so high that a capo muct be involved.