I don’t think there is any point in asking the question in OP post for now as there is no active development of Qubes Air architecture. Right now it’s just the development of induvidual blocks like sys-gui that could be used for Qubes Air later. But as I can see there is no development of Qubes Air architecture going on and Qubes Air for now is just a general thoughts on the topic without any definitive development plan existing.
So nobody can tell right now what will be with dom0 in the future.
In the future it may have restricted functionality because of different reasons for example disabling some functionality for security reasons or just because developers didin’t have time yet to make interface to securely access some functionality in dom0 like it is with Xen and CPU cores temperature right now: