Although you can make a Pale Ale in that time frame, it's never as good, IMHO, as it will be a couple of weeks later. That's true for a lot of beers.
There is a sticky about grain to glass in under 3 weeks (or something like that), and I'd read it if I were you.
As far as IPAs, I'd say no. You really want to be fully fermented and dry hopping those heavily for best flavor, which adds a couple weeks AFTER ferment is done to do it right. Dry hopping in the keg slows things (at cold temperature), and dry hopping before fermentation is complete doesn't treat the hops right. If you had a couple more weeks, it's a different story.
If it is for an event, a wheat beer or mild or brown might be the ticket, depending upon your audience. I'm always reminded that what I like (IIPAs) is not what most people (many homebrewers excepted) like. Wheat beers, milds, blondes, browns seem more acceptable to a wider audience and will ferment fast and serve well young.