Yeah, possible and best case are two different things. You can definitely have a beer that's finished fermenting in 2 months (maybe carbed, but I only keg so I can't speak to it). However, the longer you can leave a big beer on the yeast the more they can clean up the higher alcohols and off-flavors that are going to get developed. Plus, the longer you can leave them alone, the more the alcohol burn will mellow out and blend with the beer.
Of course, that's not to say there's anything stopping you! Make sure you pitch a bunch of yeast, aerate really well, and you should be able to get fermentation done in a couple of weeks. Since it sounds like carbonation might take a little longer, figure plan on getting it into bottles in a month, giving it a month to carbonate. Remember that barleywines and some higher alcohol beers are lower carbed, and a non-optimal carb might not be the worst thing. If you've got a really good reason to have it done in 2 months there's nothing wrong with this strategy. Although, if you consider the time/patience/money that it can take to brew a big beer, I hate to rush them. Besides, who wants to drink an 11% beer in the hundred degree PA heat?