Are MySQL InnoDB transactions serializable?
Per the MySQL documentation, SERIALIZABLE is: 


  This level is like REPEATABLE READ, but InnoDB implicitly converts all plain SELECT statements to SELECT ... FOR SHARE if autocommit is disabled. If autocommit is enabled, the SELECT is its own transaction. It therefore is known to be read only and can be serialized if performed as a consistent (nonlocking) read and need not block for other transactions. (To force a plain SELECT to block if other transactions have modified the selected rows, disable autocommit.)


Locking rows FOR SHARE is not equivalent to a SERIALIZABLE transaction because it doesn't protect against rows being inserted by racing transactions that could have been returned by a SELECT statement. 

The PostgreSQL docs on SERIALIZABLE provide an example case where this will occur. In your specific case, I believe MySQL's SERIALIZED isolation level will not protect you because two competing transactions can both lock the row FOR SHARE, then both can issue UPDATEs incrementing the value, one transaction will go through, the next will wait for the first to commit, but then go through. You will get a net of one increment instead of two.