I have to admit to leaning towards agreeing with Civis here, at least to a point.
Let's say that everything in Judea is unaffected. For discussion's sake. (how much that's true isn't the point). The only change is that we've started changing events elsewhere. There's no change that would cause Mary and Joseph's ancestors to be different than OTL or in different places or do different things.
So why would you be less likely to get a 1 (Jesus) than a 3 (stillborn baby girl)? You wouldn't be. You
could have #3 happen, or you could have #1 happen. Even centuries after the POD.
If, and this is the key thing, things have remained unaffected.
To me, the main thing is that they won't be. Over the course of centuries, any significant POD in two interconnected areas (even if the POD doesn't directly influence events somewhere - let's take Teutonburger Wald as something that won't specifically impact Arabia in and of itself) will see things gradually migrate from A Short History Of Dummies* and things will not be like they were by the time of Mohammad's birth (Peace be upon him) in regards to the various combination of specific circumstances. Because in a world where the Romans win there, different things will happen. Which will in turn cause other different things to happen. Which will in turn cause other things to happen. Until you're having events reacting to events that are reacting to events that weren't even possibilities from the events of OTL - you've gone into an entirely different world.
Let's use a small example. In A Short History of Dummies, I don't get an apple or take a walk instead of posting this long winded post.
1) I decide to get up from my chair, get dressed (never mind that its two in the morning), and take a walk.
And I get abducted by aliens.
I think we can trace how that makes a difference in my life that would impact the likelihood that thirty years from now I'll be a famous writer. And will impact other people.
2) On the other hand, me getting up to get an apple? Probably won't. The difference is so small as to be unable to stir a ripple - so that ripple won't impact anyone, including me.
So I suppose the point of this is that while I think changes to Judea would have to happen to have changes to Jesus, changes to Judea happening as a consequence of something where the POD is a change to Greek philosophy is not all that far fetched if we explore how people do different things and how different people do things as a result - Socrates being forgotten naturally means certain things have happened, Athens being more successful means certain things have happened, and equally importantly, both things mean that certain things
haven't happened. The combination of what has and hasn't happened of the infinity minus one (as in, not technically infinite but so broad as to be impossible to list) possibilities will be increasingly different as Sophistry Forever (the timeline we're talking about in this thread) moves on.
But in say, the Americas (which are called something different almost certainly)? They won't notice the difference for a long time.
*:
A Short History of Dummies is my sarcastic term for OTL, as one of the possible timelines that branched off from 4000 BC (when Civilization - the game, that is - starts).

Other timelines are too numerous to keep track of, but we happen to be living in the world where A Short History of Dummies took place, and everything else is "alternate".