"You could stick spaces into those 'empty' bars by swapping with something like this: while($line =~ s/\|\|/\| \|/){}"

Perhaps I'm missing your intent, but that seems like an unnecessarily complicated way to get a repeat substitution when the 'g' modifier is provided for that task:

$ perl -Mstrict -Mwarnings -E '
    my $x = q{1|2|3|||6|7||||};

    {                          
        my $line = $x;
        while($line =~ s/\|\|/\| \|/){}
        say $line;
    }                     
                                           
    {     
        my $line = $x;
        $line =~ s/\|(?=\|)/| /g;
        say $line;
    }    
'
1|2|3| | |6|7| | | |
1|2|3| | |6|7| | | |
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Using the while loop instead of the 'g' modifier is also slower:

$ perl -Mstrict -Mwarnings -E '
    use Benchmark qw{cmpthese};

    my $x = q{1|2|3|||6|7||||};

    cmpthese(1e6 => {
        while_no_repeat => sub {
            my $line = $x;
            while($line =~ s/\|\|/\| \|/){}
        },
        just_repeat => sub {
            my $line = $x;
            $line =~ s/\|(?=\|)/| /g;
        }
    });
'
                    Rate while_no_repeat     just_repeat
while_no_repeat 158479/s              --            -21%
just_repeat     201613/s             27%              --
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[Aside: the pipe (|) character is not special in the "replacement" part of s/pattern/replacement/ so there's no need to escape it.]