Hi Dana,
You should be able to consume Map Services from ArcGIS Server 10 in ArcMap 9.3.1 as a client, but you cannot create an Administrative connection to the GIS Server. New functions in 10 Services will not be available in 9.3.1 clients.
To test this you could use the following URL in an Add GIS Server, Use connection.
http://sampleserver3.arcgisonline.com/ArcGIS/services
Once connected you should see the services, and be able to preview them. Sampleserver3 is running ArcGIS Server 10.
Hope that helps,
Andrew
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