> Beijing dialect/slang "颠儿" means '(he/she) is gone', which wouldn't be readily apparent or understandable to even mandarin speakers. but the first character has the meaning "run/trip".
Old dictionaries list 颠 as a synonym of 顶 only, without a "run/trip" meaning. Most likely the character was only used for this word because both are pronounced "diān" in Mandarin and people didn't bother to make a new character, e.g. by combining [足颠]. The -儿 suffix is also interesting, because the sound modification it represents is something Beijing Mandarin speakers picked up from the Manchu during the Qing dynasty, it has nothing to do with the meaning of 儿. So 颠儿 is a relatively new addition to the written language that is not shared with non-Mandarin varieties.
The matter isn't whether I can find the proper character for everything you could say, but rather whether the spoken variety themselves can be based on written characters. In the example case you gave, it does.
The spoken varieties of Chinese can still be mapped to a set of characters, that still means there's a commonality underlying all of these variety. For instance, Beijing dialect/slang "颠儿" means '(he/she) is gone', which wouldn't be readily apparent or understandable to even mandarin speakers. but the first character has the meaning "run/trip".