Depends, if you have a split ticket, despite being one booking - then NO.
For example I travelled from Jerez to KL a couple of weeks ago - Iberia/KLM. The agent had split the tickets consequently Iberia would only check my bags as far as Amsterdam. I did ask at checkin if I could at least check my bags through to KL, but as usual, despite being a One World gold card holder, the answer from Iberia was NO (miserable gits). However on the return to Jerez, Malaysian Airlines (agents for KLM) checked my bags straight through to Jerez.
I would imagine if you have bought your tickets as all one booking, but they are not split tickets, then you should be able to.
regards
Oiler