time-pot hand

he must assume its loose enough that he wont be able to. but after talking about firing and winning regardless of cards, did you plan on not firing at this flop? do you think they were going to play back preflop knowing you just didnt want to pay time AND pick up the pot?

or is it considered a 200$ pot because you must 'put in' to raise it thus you owe regardless?
(forgive me ive never played a rake like this)