It's better to keep Li-Ion batteries charged, rather than run them down and charge them from the bottom. Some other batteries work better by draining and recharging fully, but the ideal for Lithium-based batteries is actually to keep them at around 60-80% of their maximum. Good charging circuits do this for you, so that ideal 80-ish% is actually what reports as 100%.
As far as just using wall current goes, there's no reason to take the battery out in those circumstances.