I've shut off my original iPad every night since I got it launch day. Apple just ran a diagnostic on it last week because my mother bought it in to them (as she owns it now) and they told her the battery was at 90% capacity - the Genius was shocked for a 4 year old battery.
Correlation ≠ Causation
In all likelihood, it just happens that your usage pattern is one which promotes good battery life, not that shutting down your iPad at night has anything to do with it.
And for that matter, people who are complaining about poor battery life on their devices are often to blame for it.
I was recently given an iPhone 4s when a family member upgraded because they wanted a newer phone and "the battery in this one is dead".
Well before I ordered a replacement battery for it, I decided to try using the phone for a few days. And what do you know? The battery is absolutely fine. It's just that whatever apps they use must drain it very quickly, and despite my insistence, they allow every new app to access location services, update in the background, and send them notifications.
Not surprisingly, the battery life on their new 5s is "terrible" as well.
You forgot to point out that you work in WINDOWS tech support. That's completely different. Windows tech support people tell people to reboot because it usually "solves" the problem without really having to do any work.
No, it is true of all tech support, whether it's running Windows, OS X, or some embedded device running Linux or with its own custom firmware.
My Windows PC gets rebooted once a month to install security updates, and that's it. I've never had to reboot Windows 7 or 8 to fix a problem.
I have, however, had to reboot family members' MacBooks and iOS devices quite a few times to solve problems.
After spending 30 minutes on the phone trying to troubleshoot the WiFi connection on their iPad 2 recently, including things like a full reset of the device's network settings, everything was eventually solved just by rebooting the device. Granted, it probably had not been rebooted since the last iOS 7 update, but it's certainly not a Windows problem.
I have often wondered if this was the sort of thing that ECC memory would help to prevent. Those random unexplained behaviors which rebooting the device seems to fix.
Uh, yes you can. Plug it in, then turn off the ipad. Done.
If connecting the device to a charger while it is off switches it on, perhaps that should tell you that Apple intend for it to be on while charging.