Ok I had some time to try replicate the issue: I created a server role called dataadmin. I then created a Windows group and put a login in there... called LOGINX which has the dataadmin permission role.

CREATE FUNCTION [dbo].[fnClassifier1]()

RETURNS SYSNAME

WITH SCHEMABINDING

AS

BEGIN

DECLARE @WorkloadGroup SYSNAME

--DECLARE @WhoAmI SYSNAME = ORIGINAL_LOGIN()

IF IS_SRVROLEMEMBER('dataadmin') = 1

SET @WorkloadGroup = 'gAccess'

ELSE

SET @WorkloadGroup = 'default'

RETURN @WorkloadGroup

END

GO

I then start a new session and

-- Run the below as LOGIN X

SELECT * FROM dbo.blanktable

see my attachment... it does go to the gAccess group when I login as LOGINX... Is that what you need?