My brother took his ASVAB last week. Can the recruiter tell him what jobs are actually available for him when he joins?

The recruiter can inform him what MOS's are available now for him based on his ASVAB.

The recruiter can only give you an opinion (although it could be a very accurate one). The person who can actually tell you is the career counselor at the MEPS.

As long as he's talking to an Army recruiter, the only way for him to join is by picking a job. It's not possible for him to join first and then find a job.
Other branches you can join without a job