In this case, yes:
http://www.airarabia.com/faqs#5
4. Can I check-in for my onward flight at the point of departure and reclaim my checked-in baggage at the end of the entire journey?
Yes you can claim your checked-in baggage at the end of the journey provided the entire flights are on Air Arabia. However, you need to report to the transit desk at Sharjah to claim your onward boarding card.
However, it's always worth checking with LCCs, as many have a strict "point-to-point" policy (where connections aren't even guaranteed, let alone baggage transferred...)