Yes, when you use $SIG{__DIE__} it will get called if the program would die irrespective of whether there is an eval { } around the point that is dying, as you can see from:

$SIG{__DIE__} = sub { print "die handler: " , @_ };
                                                                      
+          
eval
{
   die "DIE NOW";
};
                                                                      
+          
print "Still alive";
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/J\