Can a VM run on a Windows workstation when nobody is logged on?

Hi Guys - I'm not very knowledgeable about virtualization.  But I'm working on an application use problem and wondering if a virtual workstation on top of a physical workstation might be a solution.  Here's the problem:

We have an application that needs to run on either Windows XP or 7 after the user logs off of the physical PC.  We've tried various ways to get it to run as a service, such as srvany and the sc command.  All have failed so far.   The vendor says they have never succeeded in making it run as a service either.  I've started to wonder if instead of running the app as a service, we could run it on a virtual workstation that kicks on as a service after the user logs off the host workstation.   After the virtual workstation booted up, we would need it to automatically log-on to a network account that we would create.  At that point, an AutoIT script that I have already written would kick in, open the application, and log in a virtual user.   Then we would need the virtual workstation to shut down when anybody logs onto the physical workstation.  (If that slows down the log-in process, we can tolerate it.) So the key questions that I see would be:

1.  Can a virtual workstation run on Windows XP or 7 as a service while nobody is logged on to the host Windows workstation?

2.  Can the virtual workstation be configured to automatically log on to a certain user account.  (Probably a Windows issue more than a VM issue.)

3.  Can the virtual workstation be configured to shut down as soon as a user logs on to the physical host workstation?  (As a last resort, if I knew the process name, I could write a log-in script to net stop it.)

If anybody can point me toward resources that would answer these questions, that would be very helpful.  At this point we haven't priced or investigated any particular virtualization product.  We're just trying to find out if this concept is a viable solution before we buy anything.  We'd install the solution on about 60 workstations, possibly growing to 70, so we'd need to be careful about licensing costs.  

Thanks.