Update based on OP's comment:
To get the version of the ArcGIS API for Python package, the following snippet should work without first establishing a connection:
import arcgis
arcgis.__version__
on my machine outputs
'1.5.2'
looks like I need to upgrade
If you wish to find the version without even importing arcgis at all, Raskar Kapak's answer would be a good choice.
If you are looking for the version of the portal you are going to connect to, you can't really know it before connecting. But you can make a connection with a less heavy package than arcgisand without authenticating against the portal. You would simply use any library of your choosing that can make a POST request. If you make a POST request with the parameter f=json against the URL <portalurl.com>/sharing/rest, you will receive the following JSON response indicating the portal version:
{"currentVersion":"7.1"}
None, but it is working this morning so I must have had a typo or something. If you modify your answer (which I think makes some good points for future readers of this q&a) with your comment, I'll accept it.