Yes. You can use a browser or any other app under any context you choose, provided you have the credentials:
From the command line:
runas /user:Domain\User "C:\Program Files\Internet Explorer\iexplore.exe"
You'll get challenged for the pasword before the app starts but from then on, you're running under a different user name and context from the desktop login account. You can substitute the browser path for any application such PowerShell or SharePoint Designer, which I normally need to do on production systems to have workflows and the like run under different security accounts, etc.