Can I charge and scan simultaneously?
Yes, with the included power adapter -- but not when connected to your computer via USB.
Doxie is a standalone scanner -- that is, it's not designed for use while connected to your computer via USB. Your computer's USB port doesn't provide enough power for Doxie Go to operate.
To charge and scan simultaneously, use Doxie's included power adapter.
My Doxie Go didn't come with a power adapter
Some models of Doxie Go don't come with a power adapter. If you've got hundreds of sheets to scan in a very short period of time, consider picking one up (order links below). It gives Doxie more power than USB offers, and lets you charge and scan simultaneously for unlimited scanning in a single session.
I lost my power adapter
You can order a new one from the following sources.