Oh, oh, oh, I remember something! A certain German Let's Player who had a Splatoon series going but only very irregularly wound up completely missing one Splatfest (possibly Ninjas vs. Barbarians) - that included not voting for it. What was discovered as a result of that was that he didn't get the results announcement from the Squid Sisters. So, in a sense, if no-one participated, there'd be no outcome, as Callie and Marie wouldn't tell anyone the scores. Still, there'd surely be a result hidden somewhere in the servers or the game's coding; not sure what that'd be.
What interests me is the possibility of a genuine tie in the case of, say, votes 44-56 but battles 51-49. It's actually surprising that we haven't yet had one; it's been very close, and there was a Japanese Splatfest at some point that resulted in votes 48-52, battles 51-49, which would've been a tie under the old system (but took place when the battle bonus was 4×).