Can I use an EntityDataSource to invoke a Stored Procedure?

Try using the Function Import.

1. Right click on the EntitySet Name (the heading part)
2. Choose Add->Function Import

Here is a good blog post for you to check out. ADO.NET Entity Framework Tools: Stored Procedures, by Guy Burstein

Update: Sorry I missed the part about the EntityDataSource so I don't know of any property exposed to access a function import from the EDS, but your can try to use the CommandText property.

<asp:EntityDataSource ID="SolutionsDataSource" runat="server" 
    CommandText="DataModel.SearchFunction(@Keywords)"
    ConnectionString="name=AdventureWorksEntities">
    <CommandParameters>
        <asp:ControlParameter Name="Keywords" 
            ControlID="SearchTextbox" Type="String"/>
    </CommandParameters>
</asp:EntityDataSource>

Update: Well it seems that I have some bad news. After using Reflector to dive deep into the EntityDataSource. The EntityDataSourceView is constructed using QueryBuilderUtils.ConstructQuery, which then in turn calls context.CreateQuery<T>. What you would need to execute the function import is a call to context.ExecuteFunction<T>. There doesn't seem to be any support for the ExecuteFunction in this release, the blogs I was reading did mention that it was planned, but it didn't make it into this release, whether or not it will be in future releases I can't say.

That being said I would recommend using an ObjectDataSource, which you can construct in a way that still supports paging, sorting, etc. If you open an ObjectDataSource question on this topic send me a comment here and I'll take a look.