It would seem that it should convert them to Global Labels… that way they can have the Intersheet references as it is in Altium. Hierarchical Labels do not show intersheet references.
While Altium does allow Ports to have global scope, it will depend on how your project is configured for net identifier scope. We should shift between the conversion based on whether the project is flat, hierarchical, strict hierarchical or global.
If you file a request for this feature, we may be able to update KiCad to do this.
Use Help->Report a Bug to file the request
With all of the different Project Options in Altium, Ports always have the ability to show Cross-references (what Kicad calls intersheet references).
You can see that the only difference between Strict Hierarchical and Hierarchical is the localization of power ports.
Note here:
the Cross references are still showing, even with the scope set to Strict Hierarchical.
I will file a request for this feature.