Can Azure Functions be deployed inside a VNet?
If I created an App Service environment in a VNet and then picked that App Service Plan when creating the Function, Would that mean that the Azure Function is deployed inside the VNet and have the same restrictions etc. as defined by the VNet?
Yes, you can host an Azure function on Azure App Service Environment which provides a fully isolated and dedicated environment for securely running App Service apps or your functions. You will have fine-grained control over inbound and outbound application network traffic. So it could be restricted by network security groups.
ASEs are isolated to running only a single customer's applications and are always deployed into a virtual network. Customers have fine-grained control over inbound and outbound application network traffic. Applications can establish high-speed secure connections over VPNs to on-premises corporate resources.
VNet Integration with Azure function is a feature to use Azure Functions to connect to resources in an Azure virtual network. VNet Integration is only for making outbound calls from your app into your VNet.
In this case, you just need to deploy your Azure function in a VNet with ASE instead of VNet integration. Read Services that can be deployed into a virtual network