(And, noting the prevalence of articles from a few years ago talking about "update your fax machine firmware", I suspect you could fuzz their telco line-parser for very interesting results!)
That depends entirely on whether the handset is physically disconnected by the on-hook switch, or if a firmware exploit could remotely enable it.
Threat modeling a fax machine in the era of fuzzing-RCEs is a particularly interesting thing to consider.
"we have a high concentration of research and development personnel in China, which could expose us to market scrutiny regarding the integrity of our solution or data security features"
[0]: https://www.sec.gov/Archives/edgar/data/1585521/000119312519...
Of course, in the UK, calling Tory back-benchers "a little silly" is an understatement.
What if Huawei was Russian, would it still be "a little silly"?