"Preislamic" is a common term for near-East history. Islam is well dated, it introduced many changes and unified the region, so it's a powerful marker.
I've never encountered the word "Pre-Arabic" about the Arabic peninsula. It would be hard to define precisely. The word "arab" is probably more than 3000 years old. The Arabic languages may be older ; they're semitic languages like the Akkadian of Mesopotamia. And when did an "Arab" people or culture emerge from the semitic people and culture? I guess between 6000 BP and 3000 BP, but it was probably a long process, and nomad tribes didn't leave many vestiges.
Pre-Islamic Arabia is, as far as I know, a fairly widely accepted term. Not that different from pre-Roman Britain, pre-Columbian Americas, pre-colonial Africa, pre-imperial China, or even Pagan Europe. In all these cases a significant change took place which drastically changed the course of the region (usually some sort of unification as a nation or religion, not always peaceful or voluntary of course).
