The check-in agent "should" be able to check your bags to the final destination, but that might not mean the bags get there. I once had a ticket routing MAN-AMS-CDG-JFK-YYZ flying with various SkyTeam airlines on the same ticket. It confused the check-in agent to see so many airports on the outbound leg, but she still managed to check my bags.
Unfortunately, even though I made it to YYZ no problem, my bags didn't initially get past AMS, arriving in YYZ 2 days after I did.
My advice, make sure you have some essential change of clothes in your hand luggage!