Does the multiple value control support pulling its list from a global list, rather than hard-coding the suggested values?

it does for me, see http://msdn.microsoft.com/en-us/library/ms194977.aspx
remember to provide values in square brackets [ ]

Hmm, not sure what the deal is then...  I've got the following global list defined:

  <GLOBALLIST name="CustomerProjects">
    <LISTITEM value="[EBPC]" />
    <LISTITEM value="[SMART]" />
    <LISTITEM value="[ASI]" />
    <LISTITEM value="[BC Transit]" />
  </GLOBALLIST>

And in my work item, the field is defined as:

      <FIELD name="Customer Project" refname="Stratagen.CustomerProject" type="String" reportable="dimension">
        <HELPTEXT>Customer and/or Project</HELPTEXT>
        <SUGGESTEDVALUES expanditems="false">
            <GLOBALLIST name="CustomerProjects" />
        </SUGGESTEDVALUES>
      </FIELD>

When I try to create a new work item, I get the following error message:
---------------------------
Multiple Value Control
---------------------------
Customer Project does not have any values to list in the multiple value control. See “Work Item Tracking Multiple Value Control.doc” for details on defining a field to support the multiple value control.
---------------------------
OK  
---------------------------

Yes, it works for me, I setup a global list and the control shows the values in the drop down.
The only thing I notice in you example is that you have a value with a blank space, try removing it and see if that works.