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I think you can guess the short reply: It's an unanswerable question without defining the fuzzy stuff – in this case, "faith". 

Some (including some self-described "faithful") define faith as belief not based on evidence or reason. If that's the case, then clearly it's opposite to reason. 

"Co-exist" is another matter, though. Faith (by any definition of that word) obviously co-exists with reason on our world, just like war and peace, love and hate, wealth and poverty, and other opposites co-exist on our world. Obviously faith and reason can co-exist when each resides in a different person.

Can they co-exist in the same person? That seems trickier, but again I'd have to say "yes". As humans, we can all certainly hold conflicting views on things, conflicting ways of thinking. How about a man who is truly tolerant and open-minded to all peoples, without a thought to race or nationality – except toward those damn sneaky Greenlanders, curse them! Would we deride that man as prejudiced? Or would we say he's mostly tolerant, with a smattering of prejudice? Do tolerance and prejudice "co-exist" in him? 

Putting aside the Socratic questions. my final answer would be: Yes, faith and reason can co-exist in the same person. But it's a trivial thing, no different from the way that love and hate, selfishness and generousness, courage and timidity, ad infinitum, swirl together within any person. I'm not sure what the significance would be – other than my tentative assumption that, perhaps more easily than with many attributes, we can make a conscious effort to completely jettison "faith" from our makeup.

But again, that's all based on one definition of "faith", a word that's too often left fuzzily undefined. I'd have to ask you: Is there a definition of "faith" that changes how one would look at all the above?