Yes, there is baggage claim on both sides and it corresponds to the concourse you come from (A is claim A and B is claim B). The ME desk and pick-up is on the B side.
If your airline participates in the ME luggage program, you don't have to go to baggage claim at all - you can go straight to the claim B area and buses. If you want or have to claim your own luggage then you may have to make the trek over to A side and back to B side.
We've never traveled on an A side airline in conjunctino with ME, but have had to make the trek. Rented a car with
Avis and I think he was so upset I refused paying for an upgrade multiple times and ended up getting it for free as they didn't have a car in my paid class that he made me claim the car on the other side. Whatever...