Yes, if you use a global variable or if your signal handler is a closure with a lexical in the scope you're after. Try this simple test and see if it prints out what you expect:

{
  my $var = 1;
  $SIG{HUP} = sub { print "HUP; \$var=$var\n"; $var++; };
}

print "in main program, \$var=$var\n";
kill('HUP', $$);
print "in main program, \$var=$var\n";
kill('HUP', $$);
print "in main program, \$var=$var\n";
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Then try moving $var into the main program and declare it with 'use vars'.