Apple Watch without carrying phone

Use your Apple Watch when your iPhone is not nearby – Apple Support

Yes you can but I won't recommend doing that. The battery dies pretty fast on cellular. I usually from 65 to 15% in a single 1hour run. And I have the allaways on display turned off. Maybe that's because it uses GPS but still, that's a terrible battery life.

Also, the platform really doesn't have that many apps outside of the apple ones. And even for the apple one they are quite limited (no notes, super limited reminders, apple maps kinda sucks in most locations outside california).

So no. The apple watch is still an iPhone accessory for now unfortunately.