Can I scan with the 802.11g Airport Extreme Base Station or Airport Express?

Airport Base Station
802.11g Airport Extreme Base Station

So can you use an USB scanner with the 802.11g Airport Extreme Base Station or the Airport Express, the answer is no.

Can you use the scanning capability of an all-in-one multifunction printer when connected to the USB port of the 802.11g Airport Extreme Base Station, the answer is no.

If you connect an all-in-one printer/scanner/fax/copier type device to the USB port of an Airport base station, you will only be able to use the printing functionality of the all-in-one from a computer.

It is not possible to use the scanning function of any all-in-one printer connected to the USB port of an Airport base station - and this limitation applies to all makes and models of all-in-one printers.

You will not be able to use the scanning functionality unless the all-in-one is connected directly to the computer.

Some all-in-ones are not compatible with the Airport base station and therefore no functions will be available.

Also you can not connect an USB scanner to the USB port of an Airport base station either.

From KB-article http://docs.info.apple.com/article.html?artnum=108038#12
The USB port is for connecting a printer, not for other devices.

From KB-article http://docs.info.apple.com/article.html?artnum=107418
remember that base station printer sharing is for printing only

The base station relies on Bonjour for printing and Bonjour doesn't support network scanning.

So can you use a USB scanner or the scanning capability of an all-in-one with the Airport Extreme or Airport Express base station, the answer is a resounding no.