Of course! Families with kids go bareboating all the time. While teenagers are definitely more helpful on board, we have had sailors as young as a few months old come on a bareboating holiday in the Whitsundays.
They think they can pretty much run the show in real life, but on a boat, if the teens know their way around, they really can, which gives mum and dad some rest time. Get them to participate in the boat briefing so they know what, when and how, and you can sit back and relax.
Added bonus: most of the time there's no phone or wifi available, so they won't have their noses buried in their phones.
Primary school age kids
Great fun on a boat! They can be given meaningful jobs on the boat, like Captain of the Dinghy, Anchor Master, Navigation Officer... the list goes on. They might not be strong enough to manage sails and ropes on their own, but they can definitely pitch in and be effective crew members.
Added bonus: the skills they are learning now will likely stick with them for life, and the responsibility they are given is excellent for their confidence and sense of self.
Babies and toddlers
For many young families, the most pressing concern is if the littlest member will be safe, and will let them sleep. With regards to safety, boat bunks are often enclosed on most sides, and bolstering up the remaining side/s is easy, so the beds are great. On deck, most boats have higher molded sides and lifelines (the wires that run around the edge up to leg height) and there are in fact very few places a little one can escape. Adult supervision is always required however, so you may need to sacrifice a crew member for babysitting duties (older kids also come in handy here!). We also provide kid size life jackets for use while underway and snorkelling.
Aded bonus: What our years of experience has found is that the little ones tend to fall asleep really easily on boats. At night your anchorages are mostly very calm, and during the day the gentle rocking motion whilst underway lulls them to sleep. If you can time their midday nap with a midday move to another location, they'll hopefully sleep right through it.