Is "go bald" the same as "become bald"?
Solution 1:
Alas, no, go is not a universal substitute for become. Go is idiomatic with certain words:
Go broke
Go for broke
Go crazy
Go silent
Go naked
But with broken or sad, not so much.
Solution 2:
For the case of baldness, I would say yes. As the definition of bald at TheFreeDictionary shows, both usages are valid.
Solution 3:
"Go bald" can implicate an active choice or action. You can say "he decided to go bald" but it does not make much sense to say "he decided to become bald".