The biggest problem with throwing a great axe is how badly it fails to qualify as a improvised ranged weapon due to its weight. I'd say a battle axe (6lbs) is basically the next size up of throwable objects. 1d6 damage, range 2/4, use str and two hands to heave it. It does not return, but it does give the enhancement bonus. Its a weapon, used as a weapon (albeit improvised), in a weapon keyword power, it gets the enhancement (but obviously not the prof. bonus). A +3 battleaxe should be a better thing to throw than a mundane one, but its still a lousy choice. Of course this is only if you let heavier than 1lb be thrown.
If you can enchant a stick of wood for a +1 club, you can enchant anything you want to be more effective at fighting. You can have a +1 chair. You're being silly, and probably not very effective, but the rules let you enchant weapons, and improvised weapons are weapons. You won't buy them in any store, because its not a great idea to spend 6000 gold on a chair, but thats not really a rules reason for forbidding it. I haven't found the rules to say improvised weapons don't count as weapons for any purpose, certainly not with regards to enchanting.
Bottom line: I feel improvised weapons are weapons, and should receive all benefits (enhancement bonuses, enchantability, etc) unless expressly said not to in the rules.