If I connect a Series 3 Apple Watch to my phone, do I have to pay the cellular fee?

If you get a GPS only, the cellular carrier is not involved, and you can do Everything the cellular model can do as long as your iPhone is nearby, where nearby is say somewhere in the same 3-4 bedroom home.

If you get a cellular model, you do not have have your iPhone cellular carrier activate the Apple Watch cellular radios, and in this mode the Apple Watch will behave the same as a GPS only model. You can have your iPhone cellular carrier share your iPhone phone number at a later date, and the carrier at that time will charge you a monthly fee for sharing your iPhone phone number.

iPhone Cellular Carriers that support the Apple Watch, which models, the radio frequencies each model uses, and the country where they offer service:

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

No, the cellular does not need to be activated.