Green’s Dictionary of Slang

1. (US) very drunk.

1640		‘Mary Tattle-well’ Womens sharpe revenge 172: All sorts of people and Nations are drunk in severall formes [...] a Welchman stew’d as mellow as a Pruine [...] a Scotchman mull’d with drinke [...] an Irishman pickl’d in Vsquebaugh [...] an Englishman shall be all this and more, for he will be drench’d, stew’d, mull’d, pickled, sowz’d, and bloated.
1860		Spirit of Democracy (Woodsfield, OH) 25 July 4/1: Synonyms [for drunk] [...] drenched, soaked, mellow, having steam up, oblivious, addled.
1916		Sun (NY) 9 Apr. 10/7: [List provided by a doctor in the alcoholic ward at Bellevue — terms from ambulance drivers] [...] cock-eyed, dopey, drenched, fuzzled.
1934		B. Traven Death Ship 51: The bos’n was so well drenched that it lasted until Boulogne.
1944		P. Kendall Dict. Service Sl. n.p.: He might have been a little [...] drenched [...] but he certainly wasn’t drunk.
1966		IUFA Folk Speech n.p.: Drenched – drunk [HDAS].

2. (UK Black) bleeding (to death).

2015

67 ‘Dead Up’ 🎵 Them man high but them man soon dead up / Young niggas got the cutters out leave a big man drenched up.