As the resident Android Central code-monkey (a badge I proudly wear) I've been running on fumes and caffeine to test out the AOSP 4.1.1 code since it dropped last night. You knew I had to do it, I knew I had to do it, so there was no use fighting it. For the nerdly inclined out there, building it is easy -- just change the branch to 4.1.1_r1 and go. We'll update the tutorial in the forums as soon as we're sure there are no new nuances we need to address. In the meantime, we were curious about the local search "issue" and if Google had made any changes in the code itself to be Apple-certified™.
Building the unedited, bone-stock Android 4.1.1 and using the Google apps from the Google I/O units and their Jelly Bean update, it looks as if on-device search still exists. Our theory (it's always a guess until Big G says otherwise) is that changes to search will be done with a change to the Google Now and Search applications themselves, which are part of the closed-source Google apps. That's why we see no changes here -- we're still using the old ones. This theory was further bolstered when we learned that Sprint removed local search from the Galaxy S III, but it could be restored by using the old search box app.
There are two things to take away here -- when we see an OTA update for the Galaxy Nexus, Xoom, and Nexus S, we expect a newer set of G apps that remove the local search options, and that it will be easy enough to restore the functionality if you're willing to root your phone.
I'll keep building and tinkering with 4.1.1, and if I come across any real changes (it seems a bit faster loading apps, but the placebo affect is strong) you'll be the first to know.