Do GPS computers always need online account
Depends what you want to do with the information.  

If you just want to see your location on screen and nothing more, then no online account is required.

However if you want to push your ride recording/location to a service like strava etc, then you'll need an account with them. 

The device maker would want your information for registering the device, and warranty.  That would be a different matter, but doing this may give you access to firmware and map updates.

Finally, if your device wants internet access but has no internal cellular SIM, it might pair with a cellphone via bluetooth etc, to get internet access.  This is often done through an app on the phone.  Or you have to wait till you get home in range of a wireless AP to upload the device's recording.



I don't have a garmin personally, I use an android phone with ANT+ to talk with a HRM and a Cadence sensor.  The phone has a data internet link when in-range, and also has wireless ethernet when I'm at home.

I need a strava account, and a cellphone account, and a working internet connection at home.