Interesting question. Italian in this case is similar to English. When one has been drinking too much (but not yet drunk) you use the word "alticcio" which derives from "alto" (high) and means "rather high" , "a little high"
No, but they are similar and I wouldn't be surprised to find them together in the thesaurus.
"Hoch" generally will mean high, tall or up.
Whilst "Groß" is more broad and can mean big, tall, large, great or many.