Yes, that works as you expect. Assignments read from right to left, ie. $x = $y = $z = 10 assigns 10 to $z, then assigns the value of $z to $y, then the value of $y to $x – so all three variables end up with the value 10.

However, the code you want this for can be written cleaner without inline assignment:

sub path_to_root {
    my $self = shift;
    my $path = $self->get_branch_length;
    my $parent = $self->get_parent;

    while ( $parent ) {
        $path += $parent->get_branch_length;
        $parent = $parent->get_parent;
    }

    return $path;
}
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