Of course you could do that. Your requirement was not clear to me.

CREATE LOGIN [DOMAIN\Helpdeskgroup] FROM WINDOWS

go

USE Helpdeskdb

go

CREATE USER [Domain\Helpdeskgroup]

CREATE ROLE Helpdeskrole

EXEC sp_addrolemember Helpdeskrole, 'Domain\Helpdeskgroup'

EXEC sp_addrolemember db_datareader, Helpdeskrole

GRANT UPDATE, DELETE ON Helpdeskrole

If you are on SQL 2012, use ALTER ROLE ADD MEMBER rather than sp_addrolemember.