The question mark, in formal writing, is exactly that; it indicates that the previous statement was a question. It is not strictly a mark of the "high rising terminal inflection" normally used to indicate a question, and so it should not be used to indicate this in cases where the inflection of spoken word does not necessarily indicate a question. Most use of the inflection in cases other than a question came about in the past 20-30 years with the popularity of "valley girl" speech, which is a localized, however popular, form of speech, and not "standard" English.
However, there is an exception. Within quotation marks in a narrative, indicating a character's speech, it is generally acceptable to intentionally misspell, abbreviate, and "mis-punctuate" statements in order to convey the tone, accent, or cadence of a character's words if that is important to the narrative, or for comic relief. For instance, it has become acceptable to indicate slow, pointed, very clearly-enunciated speech using periods, such as (from The Host) "Who. Is. The. Seeker." In such cases, using question marks to indicate a character's speech inflection may be allowed for this illustrative purposes. If you do this, it has to be readily apparent that that's what you are trying to convey.