SQL Server – Mixed Mode Authentication Not Being Set

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Is there any way to avoid creating logins but get the mapping for AD users?

If you run this code:

sp_helptext 'sp_addlinkedsrvlogin'

You'll be able to find a piece of code responsible for win login creation:

-- IF SPECIFIED CHECK LOCAL USER NAME (NO NT GROUP!)
select @localid = 0
if (@locallogin IS NOT NULL)
begin
    -- share-lock the local login
    EXEC %%LocalLogin ( Name = @locallogin ) . Lock ( Exclusive = 0 )
    IF @@ERROR = 0
        select @localid = principal_id from sys.server_principals
            where name = @locallogin and type in ('S', 'U')
    else
    begin
        -- ADD ROW FOR NT USER LOGIN IF NEEDED --
        if (get_sid('\U'+@locallogin) IS NOT NULL)
        begin
            EXEC @ret = sys.sp_MSaddlogin_implicit_ntlogin @locallogin
            if (@ret = 0)
                select @localid = principal_id from sys.server_principals
                    where name = @locallogin and type = 'U'
        end
    end
    if (@localid = 0)
    begin
        ROLLBACK TRAN
        raiserror(15007,-1,-1,@locallogin)
        return (1)
    end
end

Here sys.sp_MSaddlogin_implicit_ntlogin @locallogin creates the corresponding login and its principal_id will next be retrieved by this code:

select @localid = principal_id from sys.server_principals
                        where name = @locallogin and type = 'U'

(here U indicates WINDOWS_LOGIN)

And then it will be passed to create a mapping:

EXEC %%LinkedServer(Name=@rmtsrvname).NewLinkedLogin(
            LocalID=@localid, UseSelf=@useselfbit, RemoteName=@rmtuser, Password=@pwd)

So the answer to your question is NO unless you map all your logins to the same remote_user by passing NULL as @locallogin.