It's pretty depedent on the breed, and I've never had EEs but if I leave eggs out for any more than 2 days, I swear every hen in our coop is broody. But we have mostly cochins and they are know to be very broody birds. We have about 15 nesting boxes for the 22 hens because many of them seem to stay broody even if I continue taking the eggs everyday, so nearly each one has a chicken in it all the time. But yes, that is one of the best ways to get them to be broody. I've also heard of using golf balls so that you aren't wasting eggs in the beginning, they mistake them for eggs and once they become broody, you can go down at night and switch the golf balls for real fertile eggs. So go for it but the breed makes a big difference on wether or not they'll go broody, as some commerial breeds have bred the brooding instinct out of them.