I know that having transaction attribute on a static method inside an EJB is incorrect. There won't be any exception thrown but the transaction attribute will not have any effect.
However, if an EJB has a method callMe() with a transaction attribute (let's say REQUIRED) and this method invokes a static method that is within the same EJB or another helper class, will the static method be part of the container transaction?
Yes, it will be inside the transaction. The transaction is open for that entire method and anything called inside of it will execute inside the transaction unless you use special transaction attribute methods like : NOT_SUPPORTED or REQUIRES_NEW obviously.