No, there isn't anything that can be called "wrong" about mounting the radiator externally. But like massiveoverkill said, it would pose a possible risk during the act of transporting. But, as far as the question of "whether or not a water cooled system is portable" the answer is indeed, yes.
As for effectiveness of external vs. internal mounted radiators, the answer depends on a few factors. You need to make sure that there is proper air flow through the radiator. An external radiator will not be as difficult to set up as an internal; just put a fan on it and you're good. For an internal radiator you need to make sure the air you are pushing through it isn't heated by your computer before it reached the radiator. Trully, it doesn't matter much, perhaps a difference of 1-2C, a difference which won't make or break your computer. But if you are trying to create the most efficient water cooling system with an internally mounted radiator, then you need to put a little thought in to the air flow of the case as a whole.