An Ingress controller that would contact an Application Gateway in another Azure Subscription. Is this even possible?

Yes , As YK1 said in comments it should be possible to contact another application gateway in another subscription but they should be residing under same tenant.

If they are residing under same tenant , then you can create a cross subscription vnet peering between application gateway vnet and aks vnet on different subscriptions. Then you can try to achieve the brownfield deployment for ingress on AKS.

Reference:

Create a VNet peering - different subscriptions | Microsoft Docs

Create an ingress controller with an existing Application Gateway | Microsoft Docs