1.) Mt. Ararat isn't actually mentioned in the old pre-biblical texts. IIRC, the literally translation is that the ark came to rest in "the mountains of Urartu"(sp?), which basically covers the (very large) entirety of that mountainous region.
2.) It is a very geologically active area and the mountain has violently "restructured" itself on numerous occasions in the last several thousand years, making it improbable that any structure on it would survive that long. More recent historical structures on the mountain have been routinely anihilated by this same geological activity.
3.) And perhaps most importantly, the continuous flow of glaciers scrapes the mountain clean from top to near the bottom on timescales that are measured in centuries, not millenia. Even if the ark was originally up there, it would be in a pile of toothpicks at the bottom of the mountain by now. Any structure up above the snow level would have to be young, on the order of a few hundred years old.
So I'm not holding my breath. The ark may be in that region, but the top of Mount Ararat isn't where you'll find it. The local conditions are dynamic enough that it wouldn't have lasted up there for several thousand years.