Personal story (P.S. I am not the author, I just worked in startups as well):

For me it didn't, especially when we were not prepared for it, and we know that we couldn't take the traffic if it happened.

What really killed me instead, was when our site was slowish or half-fucked during some events. And people still managed to use it harder and harder for the entire day. And we made unusual loads of money and new customers, with a crap site xD

There is of course a feeling of "how much did we miss out? that must be a lot considering how much we did get.", but it's less prominent than the feeling of "how the hell did all these people manage to pay us at all? and why the fuck did they keep using the site?". That does contradict every known blog and article out there about people just leaving.

And it not only hurts because of revenue. Slow sites also let users preceive quality and credibility as lower (Fogg et al. 2001; Bouch, Kuchinsky, and Bhatti 2000). The startup/brand will end up being seen as less interesting and attractive (Ramsay, Barbesi, and Preece 1998; Skadberg and Kimmel 2004). So being slow or offline can even have a long-lasting negative impact on the coolness of your startup.