I've never made that particular kit but I have made a few belgian style beers. The grains of paradise will add a bit of a spicy, peppery note to the beer. You will probably not be able to pick it out, but it will be there.
The higher the original gravity of the beer, the more good it will do to wait...spiced beers and strong (OG of 1.070 +) really need the time to mellow out (although the spice will start to fade if you let to go too long, like a year or so). I've made a belgian ale with OG around 1.050 and it didn't really come around until 3 months after brewing, my tripels needed about 6 months, and the Chimay Blue clone gets good at 6 months and really fine at a year.
Once you get the pipeline full, I would never ever plan to drink a beer sooner than 6 weeks from brew day if you're bottling. Even if you use mondo starters for a quick ferment, don't secondary, and force carb in a keg I gotta think that a month is a good idea. There are brewers here that I greatly respect that can turn their beers around faster than that (especially if you ferment under pressure) but I don't mind waiting a little longer. It just means I need to have more beer in inventory.
BTW, three weeks is a generally-accepted minimum time required for beers to carbonate. Longer is better.
Natural 20 Brewery
Yes, that *is* beer. Water, malt, hops, and yeast mean it's beer. Go ahead and try a glass...