edit: This was answered before the google doc's api was released. See Evan Plaice's answer and Dan Dascalescu's answer for more up-to-date information.
It looks lke you can, but it's a pain to use. It involves using the Google data API.
http://gdatatips.blogspot.com/2008/12/using-javascript-client-library-w-non.html
"The JavaScript client library has helper methods for Calendar, Contacts, Blogger, and Google Finance. However, you can use it with just about any Google Data API to access authenticated/private feeds. This example uses the DocList API."
and an example of writing a gadget that interfaces with spreadsheets: http://code.google.com/apis/spreadsheets/gadgets/