Are you in an area with a decent population of predatory birds? If so, you have the concern of attacks from above, so a cover will help to protect against that. The other benefit of a covered top is keeping your birds in - if the fence is high enough and/or if you clip one wing (one is better than both) you can reduce/eliminate that issue, but there is still a risk - it's a matter of how much risk you do/don't want to accept - really that comes down to a lot of issues in chicken keeping such as free range/vs fenced run, top cover or no, confine to coop at night or not, building with the intent of fencing in (containing your animals) or fending out (keeping predators away from yoru animals) etc - it's all a matter of a series of personal judgment calls.
and Welcome To BYC! Some good points above. X3, you will have to make them stay in the yard/run via fencing, wing clipping etc if that is where you want them, they can not really be "trained" to. Netting is used to keep chickens in and birds of prey out, it doesn't do much good against other predators. You might want to check out the Predator forum for ideas on dealing with dogs or whatever is in your area https://www.backyardchickens.com/f/13/predators-and-pests
