Is it possible to start a script as soon as an interface goes physically up/down?

Could be simulated with netwatch, not exactly same but ...

AFAIK, you can only do such thing with dynamic interfaces stemming from PPP profiles:
https://wiki.mikrotik.com/wiki/Manual:P ... Properties

Is your case time-sensitive? If not, you could use a scheduled script (with a very small interval) that checks whether or not it's active.