Minor nit: It's the other way around - the tablet contains a sophisticated charging circuit while the batteries have their own overcharging (and overload/overdrain) protection built-in (in case the device's charging circuitry fails. The battery's protector is the last, but very important final defense against an exploding or otherwise destroyed battery).
Other than that, I concur entirely with what Karel writes. Charge your tablet battery whenever you want or can, and be happy.