ernestnywang has given you the theoretical answer, and I will say what I've been able to do based on my experience.

Travelling HKG-BKK-CCU, with HKG-BKK on CX, and BKK-CCU on TG, both on separate tickets entirely, I was able to through check my luggage both ways without having to see my bags in BKK.

Although not directly related to your trip, for information sake I will also say that travelling CCU-SIN-HKG (with CCU-SIN on SQ, and SIN-HKG on CX, again on separate tix), SQ was able to check bags all the way through to HKG.