No, $1 will not be undef if the match fails. The only time they are undefined is when a match has not yet been done, or a match does not contain a captured pattern for that variable: 
#!/usr/bin/perl -w

if ("abc" =~ /(\w+)/, 1) { print "abc => $1\n" }
{ 
  print "local: $1\n";
  if ("ghi" =~ /\w+/, 1) { print "ghi => $1\n" }
  if ("def" =~ /(\w+)/, 1) { print "def => $1\n" }
  if ("[=]" =~ /(\w+)/, 1) { print "[=] => $1\n" }
}
print "general: $1\n";

__END__
abc => abc
local: abc
Use of uninitialized value at regexes line 6.
ghi => 
def => def
[=] => def
general: abc

[download]
However, a failed match returns false, so if you removed the , 1's from each of those, you wouldn't see the line for "=".

japhy -- Perl and Regex Hacker

In reply to Re: Re: Regular Expression Question by japhy
in thread What happens with empty $1 in regular expressions? (was: Regular Expression Question) by marcblecher

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