It seems like \'select count(*) from c\' in the SQL queries allowed by documentdb in the azure site and through the documentdb explorer (https://studiodocumentdb.codeplex.com/)
Currently does not exist. I had a similar scenario and we ended up adding a counter to a document attribute that gets updated every time a document gets added or deleted. You could even make these two steps as part of a store procedure or a trigger if you want atomicity.