nope, u need a valid unified ID number, which happens to be also your ARC no, but u can get a unified ID number on a tourist visa or even visa-exempt short stay by just going to NIA and applying for it.
This logic was actually challenged quite some time ago by another good chap who argued, and won against the MOTC and DMV, that the licence is something completely detached from the ARC, it is not dependent on your permit of stay and hence cannot be linked to the expiration or revokation/issuance of an ARC.
That’s why now when you get a licence issued/converted here in TW the licence is valid for 7 yrs even if your ARC is valid for just one, and when you get an APRC your licence will updated and will expire around your 70th bday if I recall correctly, since after that you need periodic health fitness exams to keep your licence.