@James ***********
really depends on the airline. Some will let you board, but some will insist on an onward ticket. Buy a throw away one or Google “onward tickets” and pay around $10 to rent one.
Train is cheap. Train ticket from Hat Yai to Padang Besar is 100 baht (approx US$3/£2.50). Third class so won’t be very comfortable for the ride you won’t be taking. 12go.asia