So let me see if I understand this. You had someone rebuild your tranny. The TCC isn't working properly so his only remedy was to unplug the connector on the side of the tranny?????

(the one that also tells the ECM what gear you're in)
The proper reply should have been "yes sir, we'll get right on that and find out what's wrong and fix it".
What was this, and AAMCO shop or something similar?
BTW, you won't burn up the tranny, but it will run hotter, and will require more frequent service intervals, etc. until you get his "fubar" fixed.
Tranny's are supposed to work when they come out of a shop. And if they don't said shop isn't supposed to find "workarounds" that defeat important features, they're supposed to fix what they screwed up.