Even if you use a property node to open a reference, it is still important to close all handles properly. Closing ActiveX references frees up memory, so you can potentially test the necessity of closing each reference by putting the code in a while loop and seeing if the required memory increases over time.
As mentioned, any reference should be closed, and in general, it's good practice to close each reference in the same place it was opened, so that you don't forget to close them.
For LabVIEW generated references, this actually matters less, because the compiler should be able to optimize those and release them automatically when they're no longer needed. For ActiveX references, however, you must do this yourself, because otherwise they will only be closed when the hierarchy goes idle. I suggest you read this for some more details. It talks about .NET, but I believe it should all apply to ActiveX as well.
But even if there is no wire comming out of a reference property, you still need to close it.