It does work. Getting 15Mbps on a TV antenna mounted to the roof. And around 4-5Mbps on the other two I have access to in my flat that's also roof mounted.
I suspect the other two have the LTE filter as while it does restrict, it doesn't block entirely so some signal can still get through. The signal strength isn't improved though compared to using a 4g antenna, and you won't get higher frequencies that they support. But if there's obstructions and you just want less lag but fine with slower speeds then a 4g antenna provides then give it a try. The adapters to use the coax cables in a 4g router are on amazon for example, though you'd need to use the cable directly without anything to secure it in place if the cable doesn't fit in the adapter you get. That'd at least be good enough for testing purposes though. And only requires unscrewing the end of the coax cable to expose the bare copper cable and plugging that into the hole directly in the adapter.
And don't ask me about if you'd need a TV license or not to use TV antennas like this because I honestly have no idea. So I don't use them myself, I only tested it out of curiosity. My 4g antenna doubles the speeds I get.