Thanks for the head up. It really seems to be related to the SQLClient and the function called in the GetReservedWords method in the MsSqlDataBaseSchema-class of NHibernate.
When creating a derived class and override this method (and of course use it in a custom MsSql-Dialect class) we can use Azure SQL Edge without a problem.
You can use the dialect like this in your NHibernate configuration:
c.DataBaseIntegration(db => db.Dialect<EnhancedMsSql2008Dialect>());
while c is your NHibernate-Configuration object.
Note: you can also derive from MsSql2012Dialect - in our use case we have a specific need not to do it ;)