For your peace of mind, I went and dug up the code behind this:

sub should_fire_birthday_notif {
    my $u = shift;

    return 0 unless $u->is_person;
    return 0 unless $u->is_visible;

    # if the month/day can't be shown
    return 0 if $u->opt_showbday =~ /^[YN]$/;

    # if the birthday isn't shown to anyone
    return 0 if $u->opt_sharebday eq "N";

    # note: this isn't intended to capture all cases where birthday
    # info is restricted. we want to pare out as much as possible;
    # individual "can user X see this birthday" is handled in
    # LJ::Event::Birthday->matches_filter

    return 1;
}

You can see that if the month and day isn't shown, the function returns "0" which is like answering "no, don't show it". So, yes, I think you are good.