Henri-
Welcome to MobileRead.
Yes, the USB cable will charge the PRS-300 (as long as the computer does not go to sleep -- some computers will turn off the power to USB when they go to sleep).
The computer does not need to have the Sony software installed for it to charge the battery. (A red LED will turn on in the top of the reader when it is charging.)
As your ebook library grows, you may want to try Calibre (
calibre-ebook.com). They also have their own sub-forum in MR. I highly recommend it.
If you have any more question on your reader, check out the Sony Reader sub-forum.
Ciao,
Ricardo