The Engineering dropout achievement is labelled as follows:
Finish 3 Corporate Islands without powering a Weapon Modification
Does powering a new weapon (but not its further actual modifications) count as powering a Weapon Modification?
Powering a new weapon is fine, but powering the upgrades isn't.
This was relatively easy to test, since ItB shows which "complete without x" achievements your game is still eligible on the achievements menu. I'll post the screenshots later.