Can a Scheduled Script call a backend Suitelet that pulls in tracking status data from a shipping carrier's webservice?

Sure.

Would I actually need the Suitelet for that or could I just make the request to Fedex's webservice from the Scheduled Script?

best option: put the Fedex-calling code into a stand-alone module, then both the suitelet and scheduled script can make direct use of it (and any other script that needs to in the future)

@scottvonduhn Ok, thank you. I'll try that