I live in a rural area. A good size UPS will run your modem for a LONG time, and is automatic. I routinely work through power outages as a result.

However, being cable, if a tree takes down a power line - chances are pretty good it can take down the cable line as well. And that happens frequent enough that I also have Starlink as a backup.

So in your case it’s probably a big, “It depends?”

Since I think most cable providers now provide phone over cable, they are generally pretty good about having service in an outage for the purpose of emergency services. And many of the combined data/voice modems they offer have battery backup options as well specifically for this purpose.