I have an award tik from STL-LAX on AA/Then LAX-HKK HKK to BKK on CX.

On Arrival in BKK I am on a paid ticket from BKK to CNX on Thai Airways with a 2.5hr connection time.

Question: Can I? and if yes Should I?, check my back straight to CNX in STL? I have heard I can claim my bag in CNX for custom purposes and just clear immigration in BKK.