Yes and no. This meaning does exist but it is antiquated English, and I have never heard it being used in conversation to mean "drunk". So, as far as current English goes, I wouldn't advise using it because nobody will understand what you mean. These days "tight" usually means the opposite of loose, or describes somebody who does not like to spend money.

yeah means drunk,, but it's slang word !

yes i look it to dictionary and i found it. cowboy...

Maybe in spoken English sometimes.