Deploy Alert Rule via Logic App

Question

I want to deploy a default health alert rule to over 400 subscriptions, so I was thinking of using a logic app to iterate through the subscription list and then deploy an ARM template to create the alert rule, using some of the subscription tags to populate variables such as the emails in the action group to send the health alerts.

So far I'm able to list the subscriptions with their tags and create a defaut resource group to host the health alert, but I haven't found a way to either directly create the alert rule with an ARM action, or deploy the custom ARM template I have created.

I wanted to know if anyone could steer me into the right course of action, because I haven't found anything in the documentation to understand if what I have envisioned is possible.