Short answer, no. The closest you might be able to come would be to create your own function that works similar to the same way AVERAGE does, but it would not run as fast as the built-in AVERAGE function.
Another approach would be to have XL change the formula as you go, using an event macro like this one. Right-click on sheet tab, view code and then paste this in:
Private Sub Worksheet_Change(ByVal Target As Range)
If Target.Count > 1 Then Exit Sub
Application.EnableEvents = False
If Left(Target.Formula, 1) = "=" Then
Target.Formula = WorksheetFunction.Substitute(UCase(Target.Formula), "MEAN", "AVERAGE")
Application.EnableEvents = True