After some experimentation, it looks as though this might be your best bet assuming you don't want to use any extra modules:

MIME::Lite->send('smtp', $SmtpServer, Timeout=>60);
eval { $msg->send };
print $@ if $@;  ### or do_something() if $@;
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This will trap the errors and allow you to continue processing but it doesn't tell you if $SmtpServer is invalid. An invalid host would return a message something like this:

Failed to connect to mail server: Invalid argument
 at mime.lite.p line ##
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If the $SmtpServer doesn't allow relaying, you might get a message like this:

SMTP RCPT command failed:
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What if the server times out? If you need to do more extensive error testing you might want to try using something like Net::SMTP, which is a subclass of Net::Cmd and IO::Socket::INET to send the message.

--Jim