Is it possible to retrieve the number of NetSuite licenses an account has provisioned with SuiteScript?

I'm not aware of an API method to do that but pretty much every NetSuite page has a taskId which you can use to resolve that page URL and then you could potentially do a HTTP GET and parse what you need from the HTML.

True, I was hoping for a native method of some sort without needing to load an entire webpage in the background.