Ok, I'll try and clear things up a little. In terms of software the N8x0 is closer to a desktop or laptop computer running linux, but in terms of hardware it's more similar to a cell phone. For the sake of miniaturization some of the flexibility of a laptop's power system is left out. On the tablet, the charging circuit charges the battery, and the system runs off the battery. Without a battery in it, it won't run.

As for your experience with it switching to "charging" after having already been charged, there are two possible explanations.
1) There are situations when the tablet can draw power from the battery, faster than the charger can add it. During the booting process is one such time, because of all the work it's doing starting up. In general, this isn't something to worry about.
2) Also, instead of constantly charging the battery, it's possible (likely?) that the hardware in your tablet lets the battery get down to 90-95% and then charges it back to 100%. However, if you plug in the charger when it's at 99% it will say charging for a second, before switching to charged. It's probably a similar case when the battery applet starts for the first time.

Executive summary: Don't worry about it. This is normal. You can use your tablet for as long as you want while it's plugged in. Also, it draws so little power while plugged in and turned on with the screen blank, that there is little reason to turn it off while it's plugged in.

-John