Can I pair an apple watch with my cell phone without a cellular plan connected to the watch?

You do not need to activate the cellular radio in the Apple Watch. When using this way, the Apple Watch will behave as if it was a GPS only Apple Watch

The GPS only Apple Watch (or a cellular that has not had the cellular radio activated) can do Everything the Cellular model can do AS LONG AS your iPhone is nearby, where nearby is generally somewhere in the same moderately sized home. The Cellular model allows you to leave your iPhone at home while you go for a walk, run, bike ride.

The Cellular + GPS Apple Watch has an eSIM and shares the iPhone's phone number, and the carriers that support the Apple Watch charge a monthly fee. In the U.S. the fee is $10 per month. Here is a list of carriers that support the Apple Watch:

https://www.apple.com/watch/cellular

Yes.