I can say "I will go", or "I'll go", and the both mean the same thing.
However, if you ask me "Can you go?", can I respond with "I'll" instead of "I will"?
Yes, that is completely fine.
I'll go sounds as plausible as I will go if someone asks you that.
EDIT:
NO, it is incorrect if you're merely answering with "I'll". "I'll" can never be used alone.
Sorry, I got confused.