The Greek text of Robert Estienne's Textus Receptus (1551) states,
καὶ λέγει αὐτῷ Πᾶς ἄνθρωπος πρῶτον τὸν καλὸν οἶνον τίθησιν καὶ ὅταν μεθυσθῶσιν τότε τὸν ἐλάσσω σὺ τετήρηκας τὸν καλὸν οἶνον ἕως ἄρτι
The Greek word in question is μεθυσθῶσιν, which is conjugated from the verb μεθύω in the 3rd person, plural number, aorist tense, passive voice, subjunctive mood.
Regarding the verb μεθύω, BDAG notes,
μεθύω (μέθυ ‘wine’; Hom. et al.; PHal 1, 193f; PGM 7, 180 πολλὰ πίνειν καὶ μὴ μεθύειν, al. in pap; LXX, Test12Patr; Philo; Jos., Bell. 6, 196, Vi. 225; 388; Just., D. 14, 6) to drink to a point of intoxication, be drunk Ac 2:15; Ox 1 verso, 15 (ASyn. 240, 40; cp. GTh 28; Unknown Sayings 69–74). Opp. πεινᾶν 1 Cor 11:21. οἱ μεθυσκόμενοι νυκτὸς μεθύουσιν those who get drunk are drunk at night 1 Th 5:7. οἱ μεθύοντες those who are drunken (Diod S 4, 5, 3; Cornutus 30 p. 61, 6; Job 12:25) Mt 24:49.—In imagery (X., Symp. 8, 21; Pla., Lysias 222c; Philostrat., Vi. Soph. 2, 1, 2 πλούτῳ μ.; Achilles Tat. 1, 6, 1 ἔρωτι; OdeSol 11:6 ὕδωρ τὸ ἀθάνατον; Philo) of the apocal. woman who has sated her thirst for blood (sim. in hue to wine) εἶδον τὴν γυναῖκα μεθύουσαν ἐκ τ. αἵματος τ. ἁγίων Rv 17:6.—DELG s.v. μέθυ. M-M. TW.
The idea in John 2:10 is that those who are drunk are not going to find bad wine as offensive to the taste as those who are not drunk (and possess a more discriminating taste).
Henry Alford notes,
The saying of the ἀρχ. is a general one, not applicable to the company then present. We may be sure that the Lord would not have sanctioned, nor ministered to, actual drunkenness. Only those who can conceive this, will find any difficulty here; and they will find difficulties every where.
The account of the practice referred to is, that the palates of men become after a while dull, and cannot distinguish between good wine and bad. Pliny (Natural History, XIV, 13) speaks of persons “qui etiam convivis (vina) alia quam sibimetipsis ministrant, aut procedente mensa subjiciunt.”1 But the practice here described is not precisely that of which Pliny speaks, nor is there any meanness to be charged on it: it is only that, when a man has some kinds of wine choicer than others, he naturally produces the choicest, to suit the most discriminating taste. With regard to the word μεθυσθῶσιν, while there is no reason here to press its ordinary meaning, so neither is there any to shrink from it, as uttered by the ἀρχιτρίκλινος. The safest rendering is that of Tyndall and Cranmer, “when men be dronke;” “cum inebriati fuerint,” Vulg.
1 John Bostock translates Pliny's remarks into English as, "[The same Cato, while on his voyage to Spain, from which he afterwards returned triumphant, would drink of no other wine but that which was served out to the rowers—very different,] indeed, to the conduct of those who are in the habit of giving to their guests even inferior wine to that which they drink themselves, or else contrive to substitute inferior in the course of the repast."
- Arndt, W., Danker, F. W., & Bauer, W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed.) (626). Chicago: University of Chicago Press.