I haven't tried your particular set up but I think it should work and ApolloSimicoe's link suggests it should as well. I made a Russian Imperial Stout with an ABV of 14% in a 10 gal cooler and based on my experience with that you should be able to get yours to work but keep in mind it may be a bit tricky compared to other batches.
You will probably have a pretty thick mash, and pray you don't get a stuck sparge. I reccomend being flexible about the recipe. For example if the amount of water you planned to add doesn't seem like it will fit don't add it, just sparge with a bit more, also in my case I held back some of the base malt (two row in my case) to see if it would all fit, if it doesn't you can add sugar to the boil to get your OG. Keep that trick in mind even if it does fit because you can use that if your numbers are off at the end of the mash. In my experience you can often add sugar to a big beer without severly impacting flavor. I would just make sure you take good notes so if you make on the fly modifications like I'm suggesting you know for next time just how much grain and water will actually fit.