I tried to add a People and Group field in InfoPath form with offline mode , and I got the following result :
Once you have opened the template outside the network you can't retrieve any users from People and Group control , it's a normal behavior because the data source connection is not available.
Meanwhile, the People and Group field will allow you to add the user's value and save the form to XML file without issue , but it can't detect theses users untile the end user connect to the SharePoint network again and open the XML file to submit it to the SharePoint.
Now the data source will reconnect again with the SharePoint site and the end user can now check the availability of these users before submitting the form to SharePoint .
Note : if the end user submits the form without checking the user's value , the form will be submitted, but the People and Group column will neglect incorrect users value (Show as Empty) that not available in SharePoint site.
the People and Group Field is Supported in offline mode because it accepts the value and allows saving , but with limitations that I have mentioned above.