Tis is where you are missing the point.
They wont.
Believe me, I spent enough time around them.
After it becomes obvious that she isnt Milo's fault (a plant) they will turn around and blame Milo et al anyway. The fact that everyone is calling her a land whale will actually be in her favour.
All those Gamergate MRAs cant deal with it when a strong woman makes a point and must silence her with shallow attacks on her physical appearance. This will actually bring them together a la Big Red, Brianna Wu, Randi Harper. Her behaviour will be forgotten, their opponent's wont be.
Some of them , like I did, will say things like "but her behaviour was ridiculous, it makes us look bad" and those people will be called MRAs and shitlords until they end up thinking its not worth the effort anymore, and end up in places like this. However, that will make the movement smaller but more cohesive as the examples will be remembered and every one will learn not to question a little bit more.
As a further example, I dont know if you had any sympathy with gamergate but if you did, how did you square the fact that nazi fucks like Davis Aruni were part of the gang?
Both sides do it, a plague on both their houses.
Well, I do think it might lead to some alienation, both between the general society and the SJW crowd and also within the SJW crowd. As you said, some people might point out how shitty Trigglypuff acted and her outburst will haunt SJWs for quite some time and the fact some SJWs will still defend Trigglypuffs behaviour might disenchant people.
But I guess (ie: fear) you're correct. They will either claim "no true SJW would act like that!" (even though they evidently do) and disregard it or jam their fingers in their ears and pretend it's all the MRAs fault or whoever their default boogeyman is.
Yet, there's still hope this will have at least some impact on them one way or another. They spawned these people, they better damn well take responsibility for it and suffer from these backlashes.
Edit:
In terms of Gamergaters, I'm firmly standing on the "Meeeeh... so what?" ground.
Like, I was on /v/ when it unfolded and in the beginning I was kinda supportive of the movement, but within a few days I realized it's just really stupid mudslinging from both sides and will most likely never achieve anything outside of internet drama - especially since it also attracted some really terrible people. And that, I can do without.
Also, a lot of the people they were so adamant against are pretty much a product of /v/ being retarded in the first place. Mind you, without /v/tards flipping their tables over FemFreq, that shit would have gone exactly nowhere. That's pretty much the reason why I stopped giving a fuck about the whole thing within a week.
Nowadays, I just wonder why they are still around. They have high claims of what they want to achieve, but in the end, it's just a bunch of jackasses pretending to be internetwarriors.
Some might actually do something of merit, some might be complete douchebags, but most are just in it to feel "relevant" or cause it's fun to them or something.
At least that's my (admittedly poorly educated) opinion on the matter.