Li-Ion cells like the one in the n800 are a very sophisticated brand of battery, as it actually features its own charging/safety circuit. What it does is cutting the charge when the battery is full, and waiting until the battery is drained enough to begin charging again. This was not the case in the old days with Ni-MH technology, as they where not subject to such extreme consequences when overcharged. Therefore the Ni-MH where generally trickle charged because of a, in most cases, "dumb" charger. My point is that a Li-Ion battery does not take any harm from being mildly recharged now and then, because it has no real memory effect. Which is again a trait of the old Ni-MH technology. It can however be dangerous to use non-authorized Li-Ion batteries as they are probably not subject to same tests and standards as the originals. Furthermore the charging circuit might not be as efficient as the original, and that can lead to overcharging and consequently explosion! I am not sure about he "fake" battery but i think it would be difficult to cheat the charging mechanism. A recommended read is:
http://www.batteryuniversity.com
It's an extensive resource for battery knowledge and care.