davecgh's answer was rather detailed and thoughtful. I mostly aggree with the thoughts. The only problem that can surface with asics is sokething similar to bitcoin's situstion. Miners and asic makers are mostly in china. First things like these couldn't be a problem but after these (possible) miners acquire a large enough voting power, those miners can collaborate in voting and steer the currency into the direction to their liking. But by the time they will be released, about 38% of the total DCR amount will be already mined.
Voting power is given to stakers, ie holders of the coin.
Those Chinese miners just mine for profit and sell, they don't care about holding and certainly not voting either.
Of course, if some of those asic miners want to hold, that means they care about the coin and should rightfully vote, no matter where they are from.
BTW, I wouldn't bet on a high correlation between asics and coin price. I think for bitcoin it was a coincidence. It was going to go up regardless. And then it also fell hard early 2014 again regardless of asics.
Asics did nothing for the price of litecoin for example