"공채에 척하니 붙었잖아" => (I/they) passed the recruitment screening just like that [spectacularly, like it's nothing, etc] You're right in thinking 척하니 doesn't mean "to pretend" here. 척 mimics the sound (onomatopoeia) of a sticky object (glued paper, dough mix, etc) slapping against a surface and sticking to it (it might make a sound similar to 척 to a Korean ear). We say 척 붙다, 척하고 (달라)붙다, etc (to stick with a slapping sound or motion). 척하니 in your phrase describes how surprisingly easily or spectacularly the person passed the exam (we commonly use the analogy of 붙다 (sticking, bonding) and 떨어지다 (falling off) for passing or failing a screening). And -하니 here doesn't indicate a reason in the sense of -하니까, but just creates a descriptive adverb which is short for '척' 하는 것 같이 or 척하듯이. 하다 commonly describes a sound or motion ("꽝!" 하다; 탕 하는 소리와 함께). 떡하니 is another common expression formed similarly, where 떡 describes how something makes its appearance unexpectedly or dramatically. - 한동안 안 보여 걱정했던 강아지가 떡하니 소파에 앉아 있다 = The missing puppy that started to worry me is sitting right there on the sofa (떡하니 adds irony and drama).

But it seems to make sense, "You're pretending to be in bondage." Doesn't it?