Associate Deans' power If a student complains to the associate dean about an adjunct faculty member, does the dean have the power to intervene?  In this case, the student is complaining because the faculty member won't accept late work, although the syllabus states that this is so.   Can the associate dean override the syllabus and force the faculty member to accept the late work?
Your question is unclear.  Does the syllabus say that late homework will not be accepted?  Does it say that late homework will be accepted (until when? for what acceptable reasons?  with a penalty?)  You also have not described why the homework was not turned in on time.  

As a general rule, as long as policies, procedures, and other rules are being followed consistently and fairly, higher-ups tend not to intervene.  It's unlikely that a dean would intervene to overturn the decision of a faculty member to not accept late homework when the syllabus specifies that late homework will not be accepted.  

It's possible that if there are unusual extenuating circumstances (e.g. the student was hospitalized after a car wreck and missed the deadline), and the faculty member is unreasonably insisting on applying the rule without considering those circumstances, then the dean might intervene.   

On the other hand, if the syllabus said that late homework would be accepted (perhaps with some defined penalty) and the faculty member refused to follow the policy in the syllabus, then a dean might well intervene.