It depends on what kind of license (Named user, Floating, etc) that you have. I think the named user licenses will let you use it with not having to 'sign in'. All the others will require signing in at some point to use it.
You will have to do one of the following
To use a license offline, open ArcGIS Pro, click on the settings button in the bottom left corner, click on the licensing tab on the left hand side, and check the box that says "take this license offline". If the named user license comes from an ArcGIS License Manager, there is a limited number of days (usually 30) the license can be checked out. If it's coming from ArcGIS Online, you can check it out for a longer period of time.
That isn't a python problem, you would still have to login to use anything associated with esri, which would include, arcpy and the arcgis modules... although the latter will allow you to perform non-esri tasks using pandas and shapely.
I use python all the time without being logged in.
The only problem you will have is if you try to use arcpy or any geoprocessing tools.
So in ArcGIS Pro when you open pro do you log in if yes there is a tick box remember me if you tick that then Pro does not log out of the scripts and I think it will also depend if you are using a floating license or a ArcGIS online named user.
If you are not using arcpy like @DanPatterson mentioned then you can just download Anaconda or Python and install the ArcGIS package.
I think that ArcPy runs independently on the ArcGIS Notebook Server, but I'm not 100% sure on that.
What I do is two-fold