Service that syncs pictures only when charging
Google+ Instant Upload offers a setting to allow uploads only when the charger is connected.

Facebook's instant photo upload does not offer such an option.

The Gallery is linked to your Google Account and thus to Picasaweb. However, there's no option within the Gallery app to restrict data transfer only when the charger is connected.

Carbonite recently started offering a mobile app, and that includes backing up photos and videos. It offers an option to use battery or not for when uploading.

So Google+ or Carbonite Mobile are your choices. (At least from the photo auto-upload services I'm aware of.)