Possible? Yes. Useful? No.
Arlo needs the server connection to manipulate the system. You don't have to have cloud recording if that's the issue - use the local storage and don't have any subscriptions. I doubt you can access the local storage without an Internet connection so you'd have to pull the drive for viewing on a computer (while risking filesystem corruption because of the inability to safely eject the drive)
It's the subscription I was hoping to avoid. The internet connection w/o monthly fees. Also, can I record to the base station in a continuous manner? These short clips are a help, but I'd really like them to be longer.
Unless you have a metered Internet connection, there's no charge for the use of Arlo without a subscription.
No, there's no continuous recording unless you subscribe to CVR (Continuous Video Recording). That's a separate sub.
Rercording length is set in your modes and rules. Read the FAQs here in the support section for full details. You can get up to 2 minute recordings per trigger or up to 5 minutes for "record until motion stops" as long as you understand that it's what the camera determines as motion, not your eyes. Testing would be in order.