Hey there GRAY Mike
Ill try to address your concerns, First off, if you're domain-joining your VMs in the Azure VNet to an AD DS solution, it's mostly going to impact those VMs themselves, not your Function Apps.
Changing your VNet's custom DNS domain for the Domain Controllers won't mess up your Function Apps' works.
Using AD DS to tighten the screws on VM security? i would say thats great, It's a good practice, especially if you've got specific security boxes to check.
As for latency issues, Domain-joining VMs and setting up AD DS shouldn't give your Function Apps any prbs They'll keep connected with Azure services. Just make sure your VNet and subnet settings align with your needs,
If this helps kindly accept the answer thanks much.