I believe that if you have an international to international connection at BKK you can have a through check in. If you fly into Thailand and the. Onto a Thai domestic flight, you need to clear immigration and pick up your bags unless on certain airline combinations.
The problem is BA policy not to interline on seperate tickets.
However sometimes an agent will do it. But no guarantees.
As for whether CX staff at BKK will pickup bags and recheck for you.....