If BoI is played on a unit that corrupts itself to do an action, such as Deathmaster Snikch or Mortella, does that mean the unit can't execute that action? I assume it can't but I just want to make sure it doesn't mean they can do it without corrupting.

Yes, you can play any attachment cards on any units, unless specified on the text. So Blessing of Isha can be played on Snitch for example, preventing him from killing anyone.