Hi Ray,
No, at the moment there is no support for that. If you would like support for a specific source code management tool, please raise a Jira issue with a feature request. There is already an issue open for basic git support.
https://issuetracker.springsource.com/browse/STS-2418
This is still more basic then what you are asking for (i.e. in here it would try to auto-enable the git support after you use the Gradle import wizard, you would still need to to do project checkout externally).
Beyond that nothing is really planned. If you raise a feature request, this allows other people to vote and see how much interest there is. If there is enough interest / votes, then something may happen.
Kris
Kris De Volder -- SpringSource