VBA UDF SUMIF with Array Parameters
A couple of things I have noticed (and I haven't tested the code):


If you make the return value a Variant, instead of Long, you can also pass Excel Errors (e.g. #VALUE!) as a result from the UDF. This would be particular useful if IfPossible is False.
You set OPERATORS up as a constant so you can check the validity of an input. But you don't use the string position at all. So, instead of Const OPERATORS As String = "&gt;,&lt;,&lt;&gt;,=", you can simply have Const OPERATORS As String = "&lt;&gt;=" which covers &lt;, &gt;, &lt;&gt; and =.
Having set and used OPERATORS, you only check the 1st character, so &lt;&gt; will never be matched.
You don't want to check for &lt;= and `>=' as well?


Codewise:

    If Not UBound(criteriaArray, 1) = UBound(critRangeArray, 1) Then
        isPossible = False
    Else: isPossible = True
    End If


Can be simplified to

isPossible = (UBound(criteriaArray, 1) = UBound(critRangeArray, 1))


Similarily:

If IsEmpty(criteriaArray) Then
    isPossible = False
Else: isPossible = True
End If


can be simplified to:

isPossible = Not IsEmpty(criteriaArray)


That entire If-Then-Else block can become:

If Not IsArray(criteriaArray) Then
    isPossible = Not IsEmpty(criteriaArray)
Else
    isPossible = (UBound(criteriaArray, 1) = UBound(critRangeArray, 1))
End If


Which, of course, you can turn around to get rid of the Not

If IsArray(criteriaArray) Then
    isPossible = (UBound(criteriaArray, 1) = UBound(critRangeArray, 1))
Else
    isPossible = Not IsEmpty(criteriaArray)
End If


Missing something here: Select Case isNumeric. That is not how the IsNumeric(val as variant) function is used. And given this is a Boolean result, a simple if-then statement will work. I am surprised this runs without throwing an error (I am taking your word for it that it works).

I am not going to go through it here (this answer is now long enough), but that case statement needs some serious rework. You have a lot of repetition and could probably get rid of at least two levels of nesting.