Is it possible for partner communities users to be able to work offline while using the Salesforce Mobile1 app?
Communities aren't available for offline access in Salesforce Mobile App (previously known as Salesforce 1).
This is documented in the Offline Access: What’s Different or Not Available in the Salesforce App documentation (excerpt below)
Salesforce Communities aren't supported when offline.
On top of this, it's only the Communities built using "Salesforce Tabs + Visualforce Communities" which works on the Salesforce Mobile App.