"I so much as look" doesn't make any sense to me

The word if is implied at the start of the sentence, which then can be interpreted as:

  • If I so much as look at a naked picture, then H.R. swoops in, and the alarm goes off.

The expression so much as here means something like even if I only do this little thing, it has negative and disproportionate consequences. Other examples:

  • If I so much as look at a cake, I put on weight.
  • If I so much as express my opinion, he starts shouting at me.