How likely is someone to get thrush after the extraction of 12 teeth?

Definitely. Thrush or candidiasis is caused by candida abbicans, an organism we all have in our entire digestive system that aids in digestion. Anything that stresses us (like haveing 12 teeth removed - or antibiotics given with the procedure) or upsets the balance of good & bad organisms can lead to thrush. See your treating dentist and they can give you a rinse or maybe pills to clear this up.