I do not understand why you need to couple "InfoPath call PowerShell scripts using the information that was submitted?"  

Collecting/extracting user information and its use are quite separate independent activities.  

You may consult [InfoPath Services cmdlets (SharePoint Server 2010)][1] about Infopath PowerShell options.  

And for collecting user information collection by and extraction from Infopath, look into "Sharepoint User Profile Web Service"    

Then. answer to your question depends whether you are going to use client IP forms which have less authentication complexities than stateless browser forms, via XMLHTTP protocol  (the browser form cannot pass through user credentials to remote data sources the same way regular Infopath forms can, via NTLM).     

**Update:**   
The simple answer to question:  

 - **"Can an InfoPath Form call a PowerShell script that makes use of the
   submitted form values?"**  

**is : "NO"**  
and I would have been extremely surprised if it was possible.   

It is not business requirements, it is requirement for security breach, business stupidity for those who order it and those who fulfill such "business requirements"   

  [1]: http://technet.microsoft.com/en-us/library/ee906553.aspx