Yes. There is no message sent to the standard error. When you use redirection to a file, the file is created when the command execution starts, so that it can rest unused if no error message comes out from the execution. If you want to redirect the standard output together with the standard error you can do this:
ls -l * > /var/tmp/unaccessible-in-spool 2>&1
that is you redirect the standard output to the file, then the standard error to the same place as the standard output. The order of redirections is important!
You can also try a different command to see the standard error file populated by an error message:
ls -l pippo 2> /var/tmp/unaccessible-in-spool
provided you do not have a file named "pippo" in your current directory.