In that case, I would definitely ask the Bangkok Airways check-in staff to check your bags through to VIE (or whatever your final destination may be). They will almost certainly agree to do so.

That way you do not have to collect you luggage at BKK, which saves time and hassle. Just make sure that you show the baggage claim receipt to the agent who checks you in for your OS flight so that they can link your luggage to your boarding pass.

You may also be able to check in without leaving the secure area by using a transfer desk, but I have not yet connected domestic-to-international at Suvarnabhumi so I don't know exactly how that would work there, but it should be possible.