Isn't something different in or to do with the output shaft and/or tail housing?
No. I believe the cooler fittings are different between the LB7 5-speed and the 6-speed, but otherwise it is (mechanically) bolt in.
Why Couldnt you though? If you changed everything over.
In order for a 2006+ Allison to work right in a LB7 with the LB7 ECM and TCM, you would need to swap in the 5-speed valve body, internal harness, NSBU and cooler fittings. You would also need to be sure to get an earlier one that has a bung in the bellhousing for a speed sensor. Of course, it will only work as a 5-speed.
To get it to work in a 03-05 (or pre-03, but that is far more involved) truck as a 6-speed, you would need to convert to all LBZ electronics (ECM, TCM, GPCM, Cluster, Throttle pedal) and top end at minumum.
That's 'converting to a stock 6-speed' in a nutshell...