Short answer: no, you'll need Windows 8 or Windows Server 2012.
A Jenkins-specific tip: I tried a number of things but did not manage to have it start apps when Jenkins runs as a service. Starting from a logged-in user account was the only way I could get it to work.
Also I'd like to recommend our Apprunner project which we developed to install, run and uninstall packages from within Jenkins.
Finally, if you're working on a Javascript-based app, you can have a look at the unit-testing-related code in our SQLite component which uses Jasmine and outputs JUnit/Jenkins-compatible test result files.