How to detect the "Server admin" user on Azure SQL Server
With Microsoft SQL Azure Databases you're user won't be a member in any server role and you won't have access to that information. So, IS_SRVROLEMEMBER will, in fact, return zeros. You only have access at the database level and not the server level--unless you build and use a SQL VM instead.

From the Microsoft documentation you can use the following to test this:

IF IS_SRVROLEMEMBER ('sysadmin') = 1  
print 'Current user''s login is a member of the sysadmin role'  
ELSE IF IS_SRVROLEMEMBER ('sysadmin') = 0  
print 'Current user''s login is NOT a member of the sysadmin role'  
ELSE IF IS_SRVROLEMEMBER ('sysadmin') IS NULL  
print 'ERROR: The server role specified is not valid.';  


However, your user will have access to the database level roles. From Microsoft documentation you can test this example:

IF IS_ROLEMEMBER ('db_datareader') = 1  
print 'Current user is a member of the db_datareader role'  
ELSE IF IS_ROLEMEMBER ('db_datareader') = 0  
print 'Current user is NOT a member of the db_datareader role'  
ELSE IF IS_ROLEMEMBER ('db_datareader') IS NULL  
print 'ERROR: The database role specified is not valid.';  


There is a caveat though, you need to be in the context of your personal database and not the master database (my database is called TESTING):



Once you're in the correct database context, the following functions, and the like, work as expected:

select HAS_DBACCESS('testing')

select IS_MEMBER('db_owner')


Note:

select HAS_DBACCESS('db_name') will return a NULL value because there's no database called 'db_name'. You can change this to the db_name() function. For example, 

select HAS_DBACCESS(db_name()) 


or, hard code the database name--TESTING in my case. 

select HAS_DBACCESS('TESTING')