The premise of your question:
the general mantra of BJJ is that technique and skill will always trump strength.
Is false. Strength can overcome technique and skill. So that's not part of my answer to your question. As to your question:
Can you be too weak to start with BJJ?
No. My reason is this: if you think in these terms then you will never start.
Too many people second guess their initial state of conditioning. Just start and let the coach know you want some direction to improve your fitness as well. Many people start BJJ because BJJ is (1) awesome + fun and (2) you get physical fitness as a bonus side effect.
Another reason is that the conditioning you need for BJJ is specific in some ways. You don't want to go down one route thinking you're "getting in shape" for BJJ, then start BJJ and realize you've frittered away your time.
Also, because you don't know BJJ, when you go practice you will be so inefficient with your energy that you will get tired quickly regardless of how fit you are.
Just go! Pair up with good people and they will dial things down to your level. DO IT.