They could also do just the opposite. Gold, gold stocks and the SPX all appeared correlated in 2008, and specifically at the time of Lehman's failure (though gold stocks of course showed much more weakness than the metal) and for about a month afterwards - after which both gold and miners significantly outperformed; $HUI had already doubled by the time stocks bottomed in 3/09, and of course they outperformed from late 07-mid 08.
Furthermore, 2001-03 was a huge bull run in the miners: $HUI increased sixfold during the same period where SPX was cut nearly in half.
In conclusion, the direction of gold stocks seems to have much more to do with a) the price of gold itself, and b) cyclical psychological/sentiment factors exclusive to miners' stocks than it does with the broader market direction. The thing is that both gold and the miners have already suffered significant declines from their peaks, comparable to 2008. I think they're likely to hold up just fine in a standard bear market, the main threat being a black swan Lehman-like absolute global panic which could cut the price of both by 25-50% in a month or two. Were this to happen I'd definitely be backing up the truck and putting on an extra-large position, betting on a quick doubling in 3-6 months once the printing presses spin up. And who knows, if a 'panic' were to take place while gold and the miners are in the early stages of another cyclical bull, rather than at the tippy-top of an eight-year bull run, perhaps they'll spike instead.