I seem to be a bit late for the conversation, but I'll post my thoughts really quickly anways.
1) I noticed you touched on the concept of the multiverse. The idea is that there is an infinite number of universes in which every possibility exists. This allows for pretty much ANY fantasy to be "real" (though the concept of the multiverse only exists in some forms of mathematics). Here's an interesting read: http://en.wikipedia.org/wiki/Multiverse
I suppose if you have any sort of fantasy you wish to be "real" you could revert to this theory and say it exists in another universe, but it's not the same type of existence we readily accept.
2) As far as anatomy, I suppose there could be certain adaptations that would allow flight. However, I believe the frame of the dragon would be similar to a bird as previously mentioned. Also, the popularized morphology of the dragon doesn't follow any sort of evolutionary path (neither do "air bladders"), so if there was a type of "dragon" it would probably have quite a different form than would be expected.
3) If we are to assume dragons exist on the premise that there is no evidence they do not exist, then who is to say a plethora of other creatures or pretty much anything could not also exist. This relates to point 1, in which I can pretty much take ANYTHING and say it "might" exist because there is no solid proof it does not exist. Clearly, there is a Flying Spaghetti Monster in the clouds, and there are also invisible giants that walk the streets of New York, and Unicorns flying in the sky, and pretty much any imaginative thing your mind could conjure. Though it is fun to entertain these ideas as possibly being reality, we must remember that there are certain limitations of this reality. Not to say that we know everything about the world around us, but there are certain limits to human perception that bind us to a specific "version" of reality.
Regardless, I do enjoy mythical creatures and find them quite entertaining.