Can it? Maybe. It’s not impossible; but it isn’t practical and most ISPs limit their shenanigans to grabbing your unencrypted DNS requests.
Will it? Probably no; aside from the previously mentioned DNS redirections; they’re not interested in most people’s packets, only in how many they deliver.
Should you care? I won’t tell you not to take precaution, but I do urge you to consider your threat model carefully and consider the tradeoffs. When Security & Privacy goes up, Convenience and Functionality WILL go down. Balance your needs. Don’t put yourself in a state of Privacy fatigue.
Are there easy fixes? Maybe. I think a VPN or using Tor would solve your concerns here anyways; it’s not required that your modem be running OSS that you can control. If you can achieve it; that’s still good for you; but it’s not something to be sweating if your modem isn’t capable and your invasive ISP is the only effective option.
Now we wait for someone to build an absolutely wonderful chat app on top of this wonderful bit of PoC code…
I genuinely hope someone does. Imagine what this could do if this was routed over Tor using Private Services.
Run this over that; and you’d have a bullet-proof text chat. Wrap a nice GUI client around all of that and you have a proper secure, anonymous messenger with no problems. With a little more build-out; you could even implement the Matrix protocol over this wire-line and basically have full inter-federation and moderation over a secure wire protocol; allowing for complete privacy and client integration.
TL;DR: Matrix over PQChat over Tor. Think about it. A Post-Quantum Dark-Matrix web.