It is quite disingenuous to disregard the military aspect of earlier Islam to its expansion, sure some (many) would follow Muhammad's vision, others wouldn't and those would call Khosrow for help if the Muslims act aggressively.
Oh no, I certainly agree that military success was crucial to the ascendancy of Islam in the Hijaz. In fact, I think if Madinah's Muslims hadn't been successful in raiding and repelling much larger Makkan forces, even regular proselytizing would have been hamstrung. Islam's social message was powerful amongst women, the poor, slaves, etc, but the Arab tribesmen who convert were more convinced by Muhammad's inexplicable military success. To use the words that the apostate prophetess Sajah said to Khalid after Yamamah - "We were many and you were few. We were strong and you were weak. We were wealthy and you were poor. This is all true, yet it is our warriors who lie dead in heaps while yours celebrate with their wives and their children. Perhaps my God hates me, perhaps your God loves you, but know that I follow what you follow once again." If the Muslims weren't winning battles, one of the main things that convinced folks that maybe this Muhammad guy has someone looking out for him is gone.
However, my contention was that by this time (I'd say that the repulsion of the Four Confederated Armies at the Battle of the Trench is the turning point), the legend of the Prophet's humiliation of Arabia's foremost power is already spreading and Islam is shifting from basically a faith spread by radicial reforming weirdos and social outcasts into a mass movement. Some degree of Islamization in Yemen, Oman, and Bahrain is inevitable unless something drastic happens. You make a good point that even if Islam comes in halfway to these regions, the tribal elites would probably see watch the evolution of Muhammad’s new (and explicitly anti-elitism/anti-tribalist) society with absolute terror and call in their Sassanid lords to stamp out the Islamic reformist preachers in their regions before the number of converts reaches a critical mass.