Yes, you have one year in which to purchase and activate your AppleCare.
Note that phone support runs out after 90 days unless you add AppleCare, so if you have a problem after 90 days, you'd probably have to buy AppleCare at that point.
You sure can. I would go ahead and buy the computer and see how it runs. If you have no problems within the first year, you may think twice before you buy applecare