No. Visual Studio 2015 (RTM) does not support SSH for Git remotes. This is true even with GitHub repositories using the GitHub plug-in (which – at present – uses the same connection mechanism for Git repositories as any other Git repository using Team Explorer.)
This is regrettable, but there are a handful of reasons why this is not available yet: the short answer is that in our opinion, providing SSH poorly or insecurely is worse than not providing SSH at all, and we would like to be very confident that any SSH implementation we provide is of high-quality.
That said, we are working on it, and making progress. Microsoft is going to begin including OpenSSH in Windows (and is a sponsor of that very fine project). However I cannot make any predictions as to when support might be available.
The GitHub extension is open source, so it’s possible that it may be able to use a different connection mechanism and begin supporting SSH before the core Git support in Team Explorer.