I am investigating the possibility of running a Nano server for a web service. I have been trying to find out if it can run an instance of SQL server 2016 in addition to IIS.
I wouldn't be surprised if the answer was a resounding "NO!", since SQL Server requires lots of features to be enabled in the underlying operating system (even installing it on a Server Core edition can be quite painful).
But since there isn't actually any information about this specific issue (and WS2016 is still being developed, including the Nano Server edition), the question is currently unanswerable. It will ultimately depend on whether Microsoft will support it or not.
Nano Server is not listed in Books Online as a supported Edition: