apple watch generation 5 cellular

No you do not have to activate cellular,you can add that anytime.If you're buying second hand make 100% sure that the person you're buying from removes the activation lock on the watch, otherwise you WON'T be able to use it.

Here is what the other person has to do;

What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else – Apple Support

No, you don't have to activate the cellular part of Watch.

All you need is your iPhone 6s or later model with you.

FYI: If the Watch is second hand, read this what the seller must do: Sell, give away, or protect a lost Apple Watch - Apple Support