Would cows survive if humans didn't eat them?

PETA and the like get up in arms about the sad life of dairy animals. And truth told, the modern factory farm does provide a brutal existence for livestock. Free range animals are healthier, happier, and therefore most likely a better dietary choice for the meat eaters among us. But I have to wonder if the fact that beef is such popular meat among us humans isn’t the key to the continued survival of today’s dairy cattle. If cattle were useless to humans and were turned loose to fend for themselves in the forests, how long do you think they would last?