Can I add cellular at any time or do I have to do that at the time of purchase?

You can buy a Cellular Apple Watch and Not activate the cellular radio. Then at a later date you can work with your iPhone cellular carrier to add the Cellular Apple Watch to your iPhone cellular plan.

The Cellular Apple Watch shares the iPhone's phone number, so the iPhone carrier needs to be willing and able to do this phone number sharing. For this service your iPhone cellular carrier will charge an extra monthly fee. In the U.S. $10 is added to the iPhone bill each month.

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

You would have to purchase a watch that is cellular capable. That and the GPS only watch are two separate devices. You cannot add cellular after the purchase of a GPS only watch.

However, the Apple Watch GPS only can do everything the cellular watch can do, much cheaper, as long as the paired iPhone is nearby.

You cannot add it later.

The cellular watch have extra hardware for cellular data connection

Only way to get it would be to get a watch with cellular