If you don't boot tethered after the initial jail break, you get the part where the Cydia icon doesn't work. I didn't see what happens if you tried to run any of the other apps, I went straight to the re-boot (as I wanted Cydia for my tweaks). So, who knows what would happen there.
If you don't boot tethered from then on, after the first reboot after jail break, the iPad won't work. It won't be bricked (cause it's fixable ... with a tethered boot) but it won't reboot or turn on. You won't get a screen and you won't see any of the apps to see if they work or not. At best, you may see the Apple logo as it sits there. At worst, you'll have a black screen. I don't even know if you can turn it off in that condition - so you may actually run down your battery.
What I think you're remembering is the semi-tethered jailbreak, which is tweak that allows you to use the iPad (after a reboot or a power up) without having to do a reboot. It'll allow you to use basic functions of the iPad, but it will not run as well until it's rebooted tethered.
In fact, my understanding is that the tweak was developed more for iPhone users who needed to use their iPhones as phones. So, if they had to reboot, this way they could have a phone until they got to their computer to fully bring the iPhone back to life. Essentially, it's a "paperclip and bubble gum" fix until you can get home for a real fix.
Hope this clarifies.
Marilyn