Hi Douglas,
AFAIK that's currently impossible to do. You might be able to do this in an extension. Perhaps you can find an active-x or java plugin that makes it possible, however, yuck!
A possible way forward is web-usb. However, I don't think there is an available driver for any scanners yet.
What you can do is write a desktop-app that does the actual scanning, but is driven by websockets rather as an UI. Then connect your web-app to this locally installed desktop-app.
If you want to write that app using nodejs, have a look at
node-sane
Regards
Sander