I wondered the same thing, but notice that they ask how much you donated to them / through them. So even if we flood in and produce hundreds of responses, as long as we're honest, the analysis will show that the people who are actually donating money look like X and everyone else looks like Y, and Givewell can decide appropriately. (And if LWers really are donating a ton to Givewell or its top charities, well, then the flooding is not a problem at all.)
Weighting GiveWell donors' responses more heavily will mean giving the opinions of people who are happy its current work disproportionate influence, won't it? It may be worthwhile to distinguish between people who are interested in effective altruism and people who follow GiveWell's recommendations.
Givewell's blog has recently begun a series of 5 self-evaluation posts (they are on the 4th right now) which discuss where the organization is at and where they're going. They're all worth a read. In particular, they build up to a survey for Givewell followers about how you'd like the organization to direct their research in the future, with options to emphasize existential risk and research even if the evidence is lower quality.