You should not have any problem to check in an extra bag in BKK in addition to those you have already checked through. I have done this many times with TG (though in SIN, not BKK) as well as other airlines in other airports and it usually worked just fine.
Sometimes it does seem to confuse check-in staff if you already hold your boarding pass and want to check in luggage. A call to the supervisor normally solved this and the luggange was then accepted. But in order to avoid this confusion in the first place i now always only get my boarding pass up to SIN first (but still check through the bags to the final destination). Then i check in again at SIN just like a 'normal' passenger. I suggest you do the same and check the bags from HGK all the way to DEL but get only the HKG-BKK boarding pass issued.