Well, you can try it, but unless you can get the sod to establish unusually-deeply unusually-fast I think you're likely to lose most of it.
Can I suggest your best bet would be to have a "sacrifice paddock" that you KNOW will go to dirt, or sand or whatever else you choose to add, and this is the chamber that the chickens walk out into when they first exit the henhouse. It then has one or more gates/popholes/whatever to allow CONTROLLED access into parts of the larger sodded area.
You then essentially do rotational/managed grazing, where the chickens are allowed onto a fraction of the grass at a time (not all of it) and only until they get it chewed down to the point of *almost being ready to begin maybe* damaging it. At that point they are rotated to a different section of the grass, and so forth and so on.
At times of the year when the grass is growing fast (at least, once it has fully established deep roots, which won't be til the end of the season this year) you MAY have enough area to keep them constantly rotating thru different grass paddocks. However if (as will sometimes happen, I can pretty much guarantee it) you find that at the point when they need to exit the "last" grass area, the "first" one is not yet grown back enough to really bear more chicken traffic, then you keep them confined to the sacrifice paddock until the grass is once again ready to accept them without serious setback. You can always chuck stuff in from elsewhere if you want them to have greens and toys while they are confined to the sacrifice paddock.
Generally you don't want the grass to get shorter than maybe 1.5-2" at the shortest (in order not to damage its ability to recover), although with chickens you also have to keep an eye on whether they're scratching around enough that it's getting *sparse* even if it's not quite that short yet.
Good luck, have fun,
Pat
