For those interested, after 24 hours of experimentation with this situation...
Ralph's answer isn't entirely correct - the 45W adapter does provide enough power to run the computer, although I suspect the computer might be running at a reduced performance level. Email and web browsing were tested most, and some graphics intensive video & one game.
If left in Sleep mode, the battery does charge, but very, very, very slowly. I have not seen any undesirable effects of this, other than the above. Seems to be okay for an emergency like I have, but doens't seem to be okay for a longer term.