Hollywood,
It is what I did with the fencing also, it works well! Just don't do what I did:

At a point the limbs of the trees are shaped to go over the top of the fencing, and you have trimmed the branches to an umbrella shape for strength (I am not doing the narrow row-form, but circles) you can them replace the larger circle of fence with one just large enough for the trunk plus a few inches. This will allow mowing under the trees without tangles in the fencing.

Don't quit while changing fencing mid-stream in the fall and leave even a single tree exposed for a minute. The deer wait in the bushes to come running out and rub their antlers all over them in revenge for years of denial. Two of my trees got nailed because I ran out of daylight and planned to finish them the next morning. Imagine my anger when I am eating breakfast to the sight of bark peeled off both exposed trees after just one stinking night. I think they hear my rebel yell in Tennessee.

The dwarf and semi-dwarf "free" varieties are massive producers, to the point you have to thin the fruit. I did not when I should have and almost lost a tree to the weight. I had to steak the darned thing up since it apparently did not have an even distribution of roots to support the weight. I've got a picture here someplace...