The reason for your error message is that the myAccList argument of checkForAs is not held. So inside of the function the expression

myAccList = Append[myAccList,resultValue]

has a list of one length on the left hand side and a list of a different length on the right hand side. A question that I then have is to ask what you actually want this function to do. If you want it to revise myAccList then there are structural ways to make that happen by adding holding attributes to the function. But if you only want to output the result, then just modify the last line as in

checkForAsRevised[aList_, element_, myAccList_] := 
 Module[{resultValue},
  If[Length[StringCases[ToString[aList], element]] > 0,
   resultValue = aList, resultValue = {}];
  Append[myAccList, resultValue]]

note that I also removed the line that reads

resultValue;

as this has no effect in the original function.