Is this not a test for a file handle?

I would say no. Neither of these statements indicate failure in any way:
    open my $oldSTDOUT, ">&STDOUT";
    open OLDERR, ">&",\*STDERR;
AFAIU, both of these statements indicate failure of file handle restoration if it occurs, but give no indication that the handle was valid prior to restoration:
    open(STDOUT, ">&", $oldSTDOUT) or warn("Can't open STDOUT");
    open(STDERR, ">&OLDERR") or warn("Can't open STDERR");

I still don't really understand the basic problem. Maybe you can find something in the following:

c:\@Work\Perl\monks>perl -wMstrict -le
"open  oldSTDOUT, '>&', \*STDOUT or warn qq{duping STDOUT: $!};
 print oldSTDOUT 'hi there everybody';
 print STDOUT '... and welcome';
 print '... to the show.';
 if (defined *oldSTDOUT) { warn 'A: *oldSTDOUT is defined'; }
 ;;
 close STDOUT or warn qq{closing STDOUT: $!};
 print STDOUT 'how now';
 print '... brown cow.';
 if (defined *STDOUT) { warn 'B: *STDOUT is defined'; }
 ;;
 open  STDOUT, '>&', \*oldSTDOUT or warn qq{re-opening STDOUT: $!};
 print oldSTDOUT 'aloha';
 print STDOUT '... sweet dreams';
 print '... and goodbye.';
 if (defined *oldSTDOUT) { warn 'C: *oldSTDOUT is defined'; }
 if (defined *STDOUT)    { warn 'D: *STDOUT is defined'; }
"
hi there everybody
... and welcome
... to the show.
A: *oldSTDOUT is defined at -e line 1.
print() on closed filehandle STDOUT at -e line 1.
print() on closed filehandle STDOUT at -e line 1.
B: *STDOUT is defined at -e line 1.
aloha
... sweet dreams
... and goodbye.
C: *oldSTDOUT is defined at -e line 1.
D: *STDOUT is defined at -e line 1.
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