I think a better sentence would be: たくさんお酒を飲むと、(私は)　つかれます。 I get tired if drink a lot of alcohol. or たくさんお酒を飲んだら、(私は)　つかれます。 (same) Because we are not tired by accident when we drink a lot - there is cause and effect. These sentences show the cause and effect clearly.

It's correct, but it should be "I drink lots of alcohol when I'm tired." (私は疲れている時にたくさん(の)お酒を飲む)

If alcohol is the thing that makes you tired, than your sentence is correct. If it's otherwise, you only drink when you want to relax, it would be as Hiromu-san has said.