To be honest, looking at the PiHole logs the TV itself hasn't tried to do much of anything. The apps on my streaming device (namely Netflix before I uninstalled it) tried, but the PiHole always caught it.
And DoT/DoH don't even add new capabilities, it's been possible to use a VPN to a popular shared hosting provider (e.g. AWS) to hide traffic for a long time before DoT & DoH became standards.