Looking at the Japanese version, I don't think that nuance was intended. The second part of that sentence was more like "and I accidentally dozed off while in that state" (of looking at the photo).
I can't tell if he's reliving his parent's romance so he can fall in love his own way, with his own manga club president, or if he's actually going to end up fucking his mother.
I mean, a child having the first crush on its mom/dad is quite normal.
Mom probably can tell. I mean she is a single mom, it's even more common in that case.