[Nogbad]

Then a bunch of Arabs rode in under this Omar dude

Are you saying there were no Arabs in Syria before Omar?
I do not think you are on solid ground there.

[Nogbad]

With regard to the Syrian connection,
this is what the Oxford History of Islam states:

(Omar) launched one set of offensives
against the Byzantine controlled territores of Palestine and Syria
home to many Arabic speaking tribes
(part of the primary audience to which the Quran had been addressed)