Join Date: Dec 2001
Location: Nomad
Programs: AA MM EP, QF Gold, UA Silver, Hyatt Globalist, Marriott LTT, HH Gold, National Exec, Hertz PC
Posts: 1,117
While CO and TG aren't partners, they're both IATA carriers and neither is known for being particularly "cheap", so I suspect they will interline. It's quite common for non-partner airlines to interline. TG had no problem interlining with Qantas for me last month, and they're also members of different alliances and competitors between BKK and Australia and BKK and London.
At the very least, it never hurts to ask at check-in and would let you avoid clearing customs and immigration and going to the landside check-in counter for your onward flight.
-m