I would hope that the x2 BE would coome with a better cooler than the base x2 which is pretty poor to begin with. You can always unlock the cores and watch the temps. I would do this before ordering a cooler as not all of them unlock successfully.
a stock cooler won't prevent you from unlocking cores. if you plan to purchase a new cooler because you believe it will help you unlock cores or expect to unlock cores, i would suggest you first try to unlock cores with the stock cooler.