A hen who is strongly inclined to go broody will do so whether or not there are even eggs to brood, a lot of the time, it's just her seasonal cycle following its natural path. Pekins and Silkies and the likes are known to brood empty nests without ever having seen a rooster. Not having roosters, eggs, or ever mating will make no difference to the compulsive broodies, though less determined hens (i.e. intensive production layer breeds) will often remain unbroody without these stimuli to provoke the instinct and hormonal cycles that otherwise lie dormant.
In short you're going to have broody hens if you have broody-natured hens, having them enjoying a normal social life with males won't make the difference. You will only have babies if you let the eggs remain in the coop where the hens can set and brood them. If they're fertile and you keep taking them out of the nest and eating them daily, the whole issue is a non issue. Leaving fertile eggs sitting to be warmed for three or more days/nights, though, will see some slight development, though they're still fine to eat by that stage.
Keeping roosters as pets where they can see but not interact with hens can lead to frustrated outlets of instinctive behaviour. Some intensive production breed roosters are known to mate with other roosters or attempt to mate with humans, since in these abnormal environments instincts still seek their natural conclusion; needless to say a rooster who views humans as mates is potentially dangerous. Females will also mate with other females, and girl-only flocks can be just as bored and aggressive as boy-only flocks. The few times I've not had roosters the hens have gotten progressively more and more aggressive. With the opposite sex as part of the flock, instead of attacking one another they think more productive thoughts, so to speak.
If you want uninterrupted egg production, but don't want those rapidly burnt out commercial layer breeds, your best bet is to breed your hens as soon as they want to set eggs, and rear another generation, and keep the hens from that to add to your flock. These daughters will lay when their mothers are taking a seasonal break, whether broody, moulting, or just resting from laying; when the daughters are ready to take their break, their mothers will be taking up duties again. This way you will maintain your flock in healthy productive state for much longer than two-year-and-done type breeds which are only productive for the short term because their breed type doesn't rest, so burns out swiftly. I never run out of eggs no matter the season because I keep differently aged mix breed and mongrel hens, and my oldest girls are still laying regularly, well past the age the layer breeds reach in working condition.
I believe intensive layer breeds are often a false economy. Mine certainly were! They reached their cut off laying point at a very young age, got injured and ill more often, (weak structurally and immunologically) were socially both retarded and aggressive, ate more food than they needed for simply producing eggs or maintaining bodyweight (absolutely terrible feed to production conversion ratio, I can support two or more currently in-lay mix breed hens, or an adult turkey, or up to five roosters on the same amount of food a single commercial laying breed hen needs). And then they died prematurely aged at about three or four. (The last part I blame on the breeders culling their older breeding stock before they checked whether or not their strain can live beyond egg production cutoff point. Not that there is any financial reward to impel them to check that, I know... Anyway, these hens all self destructed at a certain age, and I don't doubt that's a serious future genetic issue waiting to cripple industry. They suddenly lost ability to synthesize vital nutrients, and suffered neurological damage which slowly killed them. I would have thought it was disease or poisoning but it happened only to hens of that breed, at that age, from that breeder, and not just to me but also to other people who'd bought hens from that company; the diets and environments and husbandry methods were entirely different between me and these other people, so that can't be it).
Fertile eggs are complete protein sources; infertile eggs have 20-odd component protein spectrum, but lack three or so which the rooster provides. You can't taste anything amiss or offputting, lol, all you will notice is healthier eggs. In my experience a truly healthy egg has a milder, cleaner, yet more subtly flavorful taste than the rank, overly smelly ones you buy from the shops. Though lately here they are selling free range organic fertilized eggs, so that's much better. I can't stand cage eggs. Hate the taste. They're the ones that make kids and dogs fart that awful smell, too. lol.
