I would say NO since sending an email is not a domain-specific activity.
Sure, but you could get away by using a higher domain abstraction. The Domain doesn't care about emails but Notifications would be a perfect domain concept. It actually already seems to be part of the Ubiquitous Language, since you used that term in your question. So something along the lines of INotifier
instead of IEmailGateway
.
Alternate approaches could be :
Have the overarching Application Service send the email via an IEmailService interface defined in the Infrastructure.
Have the Order entity or domain service raise a Domain Event. An EmailService in the Infrastructure layer listens to it and sends the email.