It's "알지도 못할 거면서" You are VERY off: ~ㄹ 거면서, ...... = ~ anyway, and what's all the fuss about ...... 결국 일주일만에 헤어질 거면서. You were to break up eventually within a week anyway. 어쨌거나, 제가 거기 있다고 알지도 못할 거면서.... Either way, you aren't going to notice my presence there anyway.....

~(으) 면서 means "at the same time" 저는 밥을 먹으면서 TV를 봐요. =============================================================== ~ ㄹ 거면서 does not mean "at the same time" When we kind of criticize someone's former activity followed by current result we can use (~ㄹ 거면서) The sentence in the bracket is what we may want to say. 한국어 공부 안 할거면서. (Why did you buy that Korean language book? ) 일주일 만에 헤어질 거면서. (Why did you introduce him to your parents?) 입지도 않을 거면서. (Why did you buy that shirt?) Using "~ㄹ 거면서" could be a little bit offensive in many cases. But it's usually ok between close friends.