Why would a Hardware + Logic [Mental] test cause overwatch?
The moment you perform an illegal action (Attack or Sleaze), you get an Overwatch Score, or OS, that your gamemaster uses to track how much evidence you’ve been leaving in your wake. When you perform an Attack or Sleaze action, your OS increases by the number of hits the target gets on its defense test.
The Overwatch Score also increases as time goes by. If the demiGODs have time to analyze your activities, they’ll notice traces of your passing and will start to get closer and closer. Every fifteen minutes after you first start tallying an OS, it increases by another 2D6 (rolled by the gamemaster in secret).
Those are the conditions for gaining and increasing a Grid Overwatch Score. Until you take that first Attack or Sleaze action, you don't have an overwatch score, and are free to pursue the Hardware + Logic [Mental] test at your leisure. Honestly, the biggest problem as I see it is getting to that 24 threshold.
Assuming a Human with Logic 6, Hardware 6, a relevant specialization and the proper tools, you're looking at a dice pool of 14. Further assuming mathematically average rolls with diminishing dice pools (page 48), you're looking at the following results:
1st hour: 4.67 hits
2nd hour: 4.33 hits
3rd hour: 4.00 hits
4th hour: 3.67 hits
5th hour: 3.33 hits
6th hour: 3.00 hits
7th hour: 2.67 hits
At the end of the 7th straight hour you'll have reached 25.67 hits, and successfully transferred ownership. Assuming the owner is still alive and not unconscious in a ditch somewhere, and since the owner can automatically spot the icon in the Matrix, all it takes for the owner to find the physical location of his equipment is to hire a decker to use the Trace Icon on it. This would take approximately 3-6 seconds, depending on the decker.
One way to combat this is to have a counter-decker and/or pocket agent removing marks on the device as soon as they appear, but this obviously will accrue a Grid Overwatch Score. Thus, the better option is likely to ensure that any gear you steal and want to change ownership of either belongs to an owner who is no longer alive, or who will remain unconscious long enough for you to perform your task. Alternatively, keeping on the move (i.e. performing the ownership hack in the back of a van or a semi-trailer while driving around the countryside) is an option, as is travelling far enough away from the location of the owner to where it takes them longer to reach you than it takes you to change the ownership in the first place, or a combination of both.
The rules for extended tests also do allow for setting a task aside and resuming it later, though I'm not sure how wise this is in this particular instance.
In any case, to me this option boils down to "how much trouble is the item worth". If it'll fetch you a pretty penny as long as it isn't obviously stolen (i.e. doesn't belong to you) or it's something you want for yourself, then go for it. The odd Ares Predator V you took off of that corp sec guard; nah, not worth the hassle.