That's what I do. I have the phone output from my VOIP adapter in my service closet connected to the old phone lines that go throughout the house. So the VOIP adapter acts just the old POTS phone service we use to have and got rid of.
The VOIP companies tell you that their adapters don't have enough power multiple phones. But that assumes you're still using an old Bell 300 style phones with a real electromechanical ringer. All modern electronic phones use only a tiny fraction of power that the Bell 300 phones did. So a VOIP adapter can easily power a dozen or more phones. However, really long wiring in a big house can be a problem.
And so long as the VOIP adapter supports Caller ID (like mine. Almost all of them do), Caller ID on the Hopper works just fine.
One caveat, there is a chance that faxing may not work with this arrangement. Some VOIP companies restrict the bandwidth on their voice channels that makes fax not work. However, VOIP companies almost always have "fax" additional lines (for a bit more money) that do let faxing work. In my case, the regular voice works just fine for faxing even though the VOIP company cautioned that it "might" not work. Just test it out and see.
If you actually need an extra bandwidth fax line, but only want one VOIP line, just use the "fax" line for all your voice needs also.