Let's bring some maths into the equation. The first thing to bear in mind is the ascendants we play only need to be related to Desmond, not to each other. So Altair need not be related to Connor, who need not be related to Ezio, who need not be related to the protagonist of the next game (who, for the sake of ease, I am henceforth going to call Squigglepuff). That may sound rather silly but it's bloody obvious when you think about it; afterall you are related to both your parents, but they aren't closely related to one another (at least I hope not!). When you take this back, it becomes more obvious. Assuming no inbreeding, or odd coincidences, your fathers fathers fathers father isn't going to be related to your mothers mothers mothers mother. Despite you being related to both.
So that's that out of the way. Let us assume, on average through history, that the average age of parents when giving birth to a sprog is 20 years old. May seem a very arbitrary amount, but it seems plausible to me, and makes the maths easier. Hence a generation for the purposes of the maths is 20 years.
So, let's look at how many people Desmond is descended from who were alive at the same period as, say, the Third Crusade (Altair's time). That's 800 years, give or take, thus 20 generations. For those willing to check on the maths, one works it out as 2 to the power of the number of generations, in this case 2^20. That's pretty much (with some rounding) 1,000,000,000,000 (1 trillion) people he is descended from. Well, obviously not. The population of the world in 1200 was only about 360,000,000 (360 million). Hell, the best guestimate to the number of people who have ever existed is only 110,000,000,000 (110 billion). The fact is that there is going to be some inbreeding, though much will breeding with relatives so distantly related that, for all intents and purposes, they actually aren't (19th cousing 12 times removed and all that)
It means, statistically, if one was to draw a family tree that included all the people you are directly descended from, the top line would include everyone who was alive in 1200AD....1,800 ish times.
So can Desmond be descended from both an Arab during the crusades, and a Ming Dynasty Nobleman? Statiscally, he has to be...many times over.
Though it does raise the rather important question as to why the fuck Desmond is so important... I mean, seriously, having done the maths it strikes me that they could have chosen any random git and had the same result...