Short answer: No.
Longer answer: Smartthings is primarily a cloud-based system. Hardly anything runs locally. Routines don’t. Webcore doesn’t. No custom code does. The only things which don’t require an active connection to the SmartThings cloud account is some stuff in the official smart lighting feature and a little bit of stuff in the official smart home monitor feature. And that’s it. Your phone app will not work if the cloud account is not available even if you’re on the same LAN as your hub. You won’t be able to arm/disarm smart home Monitor if the cloud account is not available.
https://support.smartthings.com/hc/en-us/articles/209979766-Local-processing
On top of that, The company can and does push out firmware updates from time to time which you can neither delay nor refuse which can change even local operation. 
Sometimes we get A few days advance notice of these, but not always.
There are some mostly local home automation systems which are generally more reliable, but they may have many fewer features and integrations. So again, each person has to choose for themselves what the best match will be for their household.