Now, I don't even know if this is a proper SoPW since I understand that, to put it simply, "something strange happens with these strangely named functions, even if the docs say that they apart that detail they're not different from any other unary operator..."
Since you cannot override operators (although you can overload certain operations - but said overload magic hangs off the operand, not the operator itself), it isn't surprising you cannot override -e. Note also that the error message you get you also get if you replace '-e' with '+', 'cmp', 'feeble' or any other non-function.
Here's another way to see -e isn't a function:
perl -wce '&-e'
Bareword found where operator expected at -e line 1, near "&-e"
(Missing operator before e?)
syntax error at -e line 1, next token ???
-e had compilation errors.
It wouldn't be a syntax error if -e was a function.
Note also that perlfunc says they are operators:
-X A file test, where X is one of the letters listed below. This
unary operator takes one argument, either a filename, a
filehandle, or a dirhandle, and tests the associated file to
see if something is true about it.