It sounds to me like your book is full of a lot of strangeness.  
 
 *takes a moment to consolidate thoughts*
I don't think there's really a right answer to this question. I have come to find that there are very few hard fast rules in fiction. There are guidelines, methods that have proven to work through countless books, but there is no one-size-fits-all.
So my answer is this: It depends.
And since I don't really know much about your book, I can't really give any good advice about what to do in this situation. But I'll do my best. Forgive me if I ramble. 

So, if I came across a character in your book, a side character (one who I'm assuming doesn't stick around, or at least not much?) with a rock in his mouth, would I want to know why, or would it distract from the story?
It depends. I know, terribly helpful. Let me try to explain
Specifically, I'd say, it depends on three things. 
The book, as a whole.
Your characters.
Your audience. 
Book: Is this rock character an isolated moment of strangeness? Is the general atmosphere of the book full of such quirks? If it is an isolated moment of strangeness, I'd imagine a reader would be hungry for an explanation. But you said (I think) that it isn't, so I'd say maybe not. I don't think every strange thing that happens in your book, if your going for an atmosphere of oddity, needs to be explained. Maybe even shouldn't be. Some of them probably should be, but not necessarily all of them. Ask yourself if stopping to explain it would be distracting, or add to the interesting flair.
Characters: Are your characters used to such strangeness? Would they stop and wonder about the rock in his mouth, or would it just be part of their every day life? Are they going to wonder or care? Will they remark amongst themselves, or are they going to ask him about it? Do they already know the reason why? If they do, will they stop to consider the reasons in detail or will they just casually give a short explanation? If they aren't conditioned to that environment something like that would have a much more dramatic affect on them. If they grew up with things like that, they may not think twice.
The audience: Probably the most important thing to consider. I'm going to go out on a limb here and say that most people interested in reading fantasy are interested in learning about other worlds in some way or another. Including all their quirks and eccentricities. But how much you want to include can vary quite a bit. In this book, do you want the reader to be caught up in the world building and taken on a journey that takes them through a strange world? Or would it distract from other areas, such as characters and plot?
Hopefully that at least give some things to think about. That was very long way of saying it depends.
And I think was going to say something else, but I forgot what it was. Oh well.  
 
 I, for the record, would very much like to know why this character has a rock in his mouth.  
 
 Mistress Rwebhu Kidh wrote:
kingjon wrote:
And while there are authors who can do "infodumps" and make them interesting---Heinlein devotes a whole chapter to the construction, care, and use of space suits in Have Spacesuit, Will Travel, and besides being necessary to the plot in the end is absolutely fascinating---it's highly unlikely that you or I will turn out to be one of them. 
Yes. * grimace *
Never say never. 
