I don't think that would be possible. Once there be Muslims, they will loose the contact with the west and thus, much like Ethiopia IOTL, they will be live on their own from then.
Actually, a Thomasine Indo-Roman state would be in a far better position than OTL Ethiopia for at least two reasons.
The first reason is the fact that this Indo-Roman state is much further away from the core Muslim territories; the southern Red Sea was the only thing that stood between Yemen and Ethiopia, and the Red Sea was effectively dominated by the Arabs, whereas Arab/Islamic political influence would be rather small in southern India.
And the second reason is that the Coptic Patriarch of (Muslim-held) Alexandria was also the supreme leader of the Ethiopian Orthodox Church, and throughout much of history, the Muslim rulers of Egypt have used the Patriarch of Alexandria to exert influence over Nubia and Ethiopia.
But the Patriarch of this Thomasine Indo-Roman Church would not reside in Muslim-held territory, and therefore, the Muslims would have effectively no influence on the religious hierarchy of the Thomasine Church.
I think that Christian India would even gonna get friendly towards the Muslims instead. That choice is just better for them than to make enemy of the Muslims and got crushed by them afterwards.
And exactly how would the Muslims do that?
A strong Indo-Roman thallasocracy with a powerful fleet would be more than a match for the Muslims at sea.
And on land, the Muslim conquerors didn't reach southern India until the 14th century, and even then, the southern Indian states were (briefly) vassalized rather than conquered. An actual Muslim conquest of southern India didn't happen until the 16th century.
If the Indo-Romans would make an enemy of the Muslims, they'll still be able to last for many centuries againest them, even if the Muslim conquest of India still happens ITTL and proceeds much like it did in OTL.
And there have been nations in the past that were in a far worse position againest the Muslims, and yet successfully resisted for centuries (Makuria comes to mind, as does Ethiopia, the Georgian kingdoms, and even the local Zoroastrian nobles in the Alborz mountains and Tabarestan, who did not submit to the Muslims until the 9th century).
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On a related note; if the Indo-Romans would become enemies of the Muslims, then it is actually not unlikely that this would slow or halt the spread of Islam in south and southeast Asia for centuries, perhaps even indefinitely, judging from the fact that Arab Muslim merciants in southern India and South Indian converts played a very important role in the Islamisation of southeast Asia in OTL.
In OTL, Islam became a major religion in the Indonesian archipelago during the 14th century, and Islam had taken root in the region during the 13th century with the rise of the first Muslim city states on the peninsula and Sumatra.
But the thing is; would Islam still take root in southeast Asia in a TL where both the influence of Arab merciants as well as the spread of Islam are being frustrated/halted by a Christian Indo-Roman state that effectively controls the trade routes between southeast Asia and southwest Asia?
IMHO, Islam still could take root in southeast Asia in such a scenario (quite possibly via Bengal, provided that the Muslim conquest of India still happens as in OTL) - but wether it could become the dominant religion there just like in OTL is a very different question.
If Islam is not firmly established in southeast Asia when the Europeans begin to dominate the area, then the odds are that Islam will never become the dominant religion there at all
I don't think that'll be possible. To be able to go to Malabar, the closest route is first to Yemen or Hadramaut(basically southern Arab coast) then board on ship from there to Malabar. Muhammad had never traveled to Yemen when he was young IOTL. And I doubt that he had ever been Yemen for just once in his lifetime. Mecca wasn't in good terms with Yemen in those days anyway.
I'm inclined to agree that Mohammed propably wouldn't end up in this Indo-Roman colony (it would be more likely that he ends up in Syria, and IIRC, he had been Syria when he was young IOTL).
In my opinion, it is more likely that Mohammed would be butterflied away alltogether, because a strong Roman colony in India would result in a (much) stronger Roman presence/influence in the Red Sea, which could very well affect the economic and political situation of the nations and territories surrounding the Red Sea, including the Hijaz.
For example, it's quite possible that a coastal city or village in the Hijaz that remained fairly unimportant during this period in OTL, would become an important port on the trade route between the Roman Empire and its Indian colony, and that, say, the man who became the great-grandfather of Mohammed in OTL decided to work in that port instead, thus changing his life, and quite possibly resulting in him marrying a different woman than in OTL, resulting in Mohammed not being born.
