Apple watch cellular compatibility

They do not appear to be a compatible carrier:

Apple Watch - Carriers - Apple

You should consult Consumer Cellular for a definitive answer, though. They're always going on about how great their customer service is. Perhaps this is a good time to test that.

However, you can still use the watch connected to your phone. You just won't be able to use the cellular capabilities.

This is a list of carriers that support the Apple Watch. Your iPhone "MUST" be using one of these carriers. It does not count if your carrier piggy backs on top of another carrier.

If the company you pay money to is not listed, then you cannot add a cellular Apple Watch to your carrier

And you MUST use an Apple Watch model supported by the carrier.

Note, if you always have your iPhone nearby, you can do EVERYTHING with a GPS only model that you can do with a cellular model, ad the GPS only Apple Watch will just use the iPhone's radios.

This can be helpful figuring out if you really need a cellular model

What the Apple Watch GPS-only can do without an iPhone

https://support.apple.com/en-us/HT205547

https://www.imore.com/heres-what-apple-watch-can-do-without-iphone