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.....