"He went into counseling."
Could the above have two meanings?
1. "He became a counselor after getting the education and licenses."
2. "He received help from a counselor."
To me it suggests only the first of your paraphrases.
I would only think it meant the second.
Context helps, of course.
I would say yes, quer (and welcome to the forum).
'He failed his psychiatry exams so he went into counselling (BE spelling).'
'The judge suspended the sentence on condition that he went into counselling.'
Rover