I went to someone's house the other day and she has two absolutely huge Doge de Bordeaux. I watched them sitting contentedly in the garden surrounded by a menagerie of ducks, turkeys and hens which was an absolute delight. So really I think it is down to the type of dog you have. I have two gundogs who have bird-shaped spaces in their brains and so will never be trustworthy with the hens but I am sure that other less 'bird-orientated' breeds would be fine once they are used to them.
As to problems with land with a path through it, I sympathise. I had a similar problem in the UK. I had a steep moorland paddock that I used to exercise my dogs safely. There was a farm gate at the bottom and a small pedestrian gate at the top which gave out onto a superb hilltop walk. However it wasn't a right of way (even though I had heated exchanges with people who insisted it was! The right of way actually ran alongside the outside edge of my fencing but over time people seemed to have forgotten that). However, I was happy for people to use it, provided they shut the top gate. That was all I asked but it was obviously too much to ask. Eventually I got so fed up that I padlocked the top gate. I couldn't risk my Pointer escaping as she was terrible with stock and being high up on the moors the top of the paddock was frequently submerged in fog so it wasn't possible to see if it was shut.
Now with the land I have here, the only problem I have is hunters entering my land without permission (normal here!!!). Once I get the fencing and warning signs up, the Pointer will see to it that they don't do this again, at least not without having to count limbs/fingers on the way out!!!