I have seen a pumpkin converted into a mash tun, there should be no doubt that it can work.
I would be weary of the the mash tun soaking up wort during the mash. Also, it would be hard to clean the barrel once you do mash in, nasty stuff will grow on the wort that is stuck in between the cracks of the barrel and could influence the finished beer.
The boil will kill the microbes the byproducts they produce during their growth cycles will survive the boil, and contribute to poor head retention and impact the flavor.
On the plus side I wonder how much oak flavor this will impart on a beer, and if it would be different than aging the beer in a barrel? I would think that the heat of the mash would make the oak leach more flavors into the beer.
I would not do it more than once in the same barrel.