(1) If you see the red light on or flashing while connected to the XIM via cable, then yes it is charging....
(2) But if you're using your NAV wired then why are you worried about charging it O_o?
1. Thx. I don't recall seeing the red light on when connected through the XIM.
2A. Because it's a huge time waster; probably around 30 min to charge fully. I have very little free time, married with kids and full time job. So I can't realistically just turn on my PS3 anytime I want. I stop playing at around 1am, so I want to turn off my PS3 and go straight to bed before waking up for work early in the morning instead of waiting 30 min to charge a stupid controller.

2B. Because it could potentially disable mid-game due to lack of battery. Not only would that be frustrating to die like that, but that would mean I would have to stop playing for 30 min just to charge it back up again.
So basically what I do is charge it up directly to PS3 for a few minutes before and after each session. But if I forget to do this, or dont have the time or patience, eventually I will be left with a dead battery which is not cool. So that is why I'm worried about charging it.
