Well, well, as you say, life is strange. For I tell you I should not wonder if Euripides' words were true, when he says:
“Who knows if to live is to be dead,
And to be dead, to live?"
and we really, it may be, are dead; in fact I once heard sages say that we are now dead, and the body is our tomb....
The word used for 'body' is σῶμά and the word used for 'tomb' is σῆμα, so we are dealing with a play on words.
This association between the body and the tomb is given a more expansive development in the Cratylus (400b-d):
Now what shall we say about the next word?
You mean “body” (σῶμα)?
I think this admits of many explanations, if a little, even very little, change is made; for some say it is the tomb (σῆμα) of the soul, their notion being that the soul is buried in the present life; and again, because by its means the soul gives any signs which it gives, it is for this reason also properly called “sign” (σῆμα). But I think it most likely that the Orphic poets gave this name, with the idea that the soul is undergoing punishment for something; they think it has the body as an enclosure to keep it safe, like a prison, and this is, as the name itself denotes, the safe (σῶμα) for the soul, until the penalty is paid, and not even a letter needs to be changed.
So we have here three different etymologies of the word for 'body':
(1) σῆμα (tomb, grave, cairn, barrow)
(2) σῆμα (sign, mark, token, omen)
(3) σῶμα (safe)
There are indeed natural verbal connections among all of these, going beyond mere similarity in sound. σῶμα had already begun to be applied to all kinds of bodies, as here, but in Homer it only applies to corpses. σῆμα (tomb) obviously relates to this. σῆμα (tomb) and σῆμα (sign) are not homophones -- they are the same word in different usage, since a tomb is a sign marking a burying-place. The third derives a word from σώζω, which means to keep safe, and, indeed, is often used in the sense of 'to keep alive'. Socrates associates the third with a prison-house, δεσμωτήριον and the Orphic view that our souls are in our bodies as a punishment. As James Adam noted long ago in his The Religious Teachers of Ancient Greece, it is entirely plausible to suggest that the third usage might lead to the first usage as a kind of abbreviated form.
The flipping of life and death, as we get it in the Gorgias, is not unknown elsewhere in Plato. I've noted before the instance in the Allegory of the Cave in the Republic in which, having condemned Homer for having Achilles claim that the world of the living is better than the world of the dead, he nonetheless quotes the exact same passage -- for the Allegory of the Cave flips the underworld myth. We are the shades in the underworld, the world of the dead; and it is better to be out in the light than to be as we are.