I guess most people would trade Dash -> BTC -> Fiat. By far, Dash/BTC is the largest market, Dash/USD is tiny compared to it. I don't think there will be a relevant impact of a massive Dash -> BTC movement into the BTC/USD price, but a large "Dash bank run" into fiat via BTC could affect the price to the downside.
Volume of Dash was 25-75 million per day in the last week, so there is some money in there. Maybe not sufficient for a large crash, but it could cause a correction, above all if - as you speculate - there were massively masternodes withdrawing from the Dash ecosystem.