After the first match, \G will no longer be matching at the start of the string (^), so the output will just be

whitespace
done
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Both ^ and \G are called "assertions". The Assertions section of perlre has quite a bit to say about \G and provides links to further information.

It is certainly possible to use both of those assertions in the same regular expression. In fact, changing each instance of '^\G' in your code to '^.*\G', provides your desired output.

Here's my test code:

#!/usr/bin/env perl

use strict;
use warnings;

my $string = " a 1 # ";
my $i = 0;
while () {
    if ( $string =~ /^.*\G\s+/gc ) {
        print "whitespace\n";
    }
    elsif ( $string =~ /^.*\G[0-9]+/gc ) {
        print "integer\n";
    }
    elsif ( $string =~ /^.*\G\w+/gc ) {
        print "word\n";
    }
    else {
        print "done\n";
        last;
    }
}
[download]

Output:

whitespace
word
whitespace
integer
whitespace
done
[download]