I have a remote base where stations can log in with DTMF touch pad.
Does this remote base transmitter need to send out a CW ID?
I believe that according to §97.3, logging in to a remote base through the Internet is considered remote control. Therefore, the amateur logging in is the control operator, and the normal identification rules apply. The base does not need to identify separately.
That said, if there's a repeater linked in to the system, such that transmissions are automatically rebroadcast on a different frequency, I think that repeater would need to auto-identify as per usual. This site also indicates (search for 'remote base' within that page) that you'd need to approve this entire setup (a remote base accessed through an otherwise publicly-available repeater) with your local frequency coordinator.