In the event of a tie, the the lower court is the tie-breaker. Having an even number of justices doesn't break the court, and even if it did, it'd be another long while before this case could be appealed that high anyway.

Even if we're to believe the rhetoric that the Senate isn't going to appoint any candidate, nobody's even been nominated yet, so the idea that the whole system is broken may be true, but not for the reasons speculated.