Technically, it is possible to have AAD tenant without Azure Subscription but not vice versa. When Dynamics 365 X subscription is purchased the purchase is done in a context of a particular AAD tenant identified by the user, from a particular already existing AAD instance, a customer is using to sign-in. So purchasing Dynamics 365 X subscriptions doesn't result in new AAD Tenant creation neither it results in any subscription "automatically given" to the purchaser.
Depending on what kind of Commerce (cloud based vs on-prem) is needed, there are number of possibilities. In case of Cloud deployment the HQ part of the solution could be deployed in Microsoft managed/owned Azure Subscription as well as in customer hosted Azure Subscription brought up by the customer. So, if you do want to have full control over the HQ's hosted environment - you could bring your own Azure Subscription which you should purchase separately unless you have it already but if you are fine using the one managed by Microsoft, as described in the above link, then you don't have to bring your own Azure Subscription.
There is also on-prem flavor where everything (including Commerce components) is hosted inside environment(s) owned by the customer, those don't require any Azure Subscriptions at all.
