My first thought was that those who would choose to adopt a pet based on a viral social media campaign would necessarily make irresponsible pet owners, and inevitably dump the cats within a couple months.

(Caveat to this analysis: Overall there is around a 90% adoption retention rate after 6 months (and it surprised me from my experience that retention skews higher for younger people), so any "idiot effect" may not be too dramatic even in the worst case. [Full analysis in Hawes etal 2020])

But then you have to think that -- for example -- at least some of them are people who, unlike most pet owners, maybe never grew up around pets and never considered before having one. So let's say we get 50/50 from these viral campaigns -- 50% of adopters are terrible and release the animals into the street once they lose their Kony 2012 hype, while the other 50% become solid pet owners who might otherwise not have been. The shelter, now empty, can fill up with street and rejected animals again, which at least mitigates the losses of the former 50% (animals in == animals out), while the latter 50% is a complete gain. (Well, a gain excluding externalities, which can get really messy and is poorly understood.)

So as long as you introduce at least a few responsible new people to pet ownership, these campaigns are a net benefit, regardless of idiots.