Most people will be speaking Syriac, an evolution of the Aramaic language, though of course many of the educated/bureaucrats would have also spoken Greek and Persian depending on which empire they were in. Syriac is a Semitc language, but is from a different branch of the language family and so won't be entirely intelligible to native Arab speakers.

I'd also like to clear up something about Arab nomads, as we have evidence that many Arabs were not nomads by the seventh century. Both Syria and Iraq had a substantial Arab minority - Arabs were not just a people living outside the Roman and Persian empires, but often settled within them as well. Even on the borders imperial influence meant that there were organised Arab polities already, such as the Ghassanid and Lakhmid confederations of the sixth century, both of which built monumental buildings and the latter even had a city, Hira, as both groups were amply rewarded for their military service to their respective patrons. This is also ignoring the traders who would ply their trade across the whole region. Arabs were not alien to the central Near East, but a people living within a deeply connected and economically flourishing world.

There were some arabic speaking people in the area, e.g. the kkingdom of the nabateans, who were allies/vassals of the Byzantine empire. Their kingdom was roughly in modern day Jordan.

Nomads travelling further north, I don't know, but it's possible. Maybe somebody else knows more :)

The main language in the are would have been Aramaic, a nort-wester semitic language, so related more closely to hebrew, phoenician and caanan languages than to arabic. A time traveller would not be understood!

The arabic spoken at that time was pretty different as well, of course. The Nabateans were the first to use what would develop into the modern arabic alphabet, but their old dialect was different from how arabic became standardised post-muhammed