No, because when some miners shut down the difficulty will drop and the remaining miners will get a larger proportional reward, thus retaining profitability. There is no price so low that the system will stop working entirely.
Also, to everyone who's ever thought I was joking when I warned friends that the price was about to tank because I am, as a rule, on the losing end of every market shift, two days ago I was told first of next week I'd have a big invoice to pay in BTC. So expect the price to keep going down until about an hour after that invoice has been paid, and I'll let y'all know when to buy in at the bottom.