This is helpful. So SICF is cross-client. So that tells me that I need to create a new SMTP host for every host beyond SAPConnect.
SAPConnect is a default SMTP host that comes with SAP ECC out of the box. I can use this one for my first client. However, I will need to create a new SMTP host for the other clients.
I will also need to have a separate user in each client in order to be able to use the service.
My question has been resolved.
Thanks Yuksel!