Access 2010 introduced support for Data Service which in theory would do what you just described, provide you a table that represent data populated by a web service. Unfortunately, this feature involves a setup with SharePoint to provide the interface to the web service (well, I suppose if the web service you mentioned already exposes the same interface, you could connect to it directly but I think the likelihood of such web service available is low compared to more common protocols such as SOAP or REST).
Since the Excel Web Query already does what you need, surely you could get this via Access automating Excel, no?