Actually, I pulled that out of my a$$. But now that I think about it, I would guess that it would make a huge difference.
From my understanding of the manufacturing process, the leaves are arranged in such a way as to allow the smoke to flow freely from the lit end. Think of the leaves as arranged as little funnels/umbrellas where all fluid is smooth one way, but it is not smooth going the other way. I have, in a previous exeriment, lit the wrong end of the cigar (OK, I was freaking drunk) after cutting it, and it did not draw well and the flavor profile was all wrong.
BTW, I call most of my mistakes "experiments."
If you look closely at a standard cigar and see how the wrapper covers itself as it goes from foot to head (foot is what you light, head is what you... uh, the other end) you can see that it is wrapped that way to prevent it from unraveling as you smoke it. If you smoke it backwards, it may stay together because of the vegetal glue, but it is more likely to come apart.
The two eggs that I have smoked were very good. However, I have to admit that it took me a few minutes to figure out which is the head and which is the foot.