This is a very strange issue, and I expect we'll see some clarification of it at some point as weapon-implements become more common.
The "weapons don't get powers when they're implements" thing should be taken with a grain of salt, because it doesn't make sense in a pretty broad spectrum of uses. It wouldn't apply to the daily power of a Holy Avenger, for example. Why? Because weapons that are being used as implements don't stop being weapons; they're both a weapon and an implement, at the same time, all the time. Just because you use your Holy Avenger to cast a spell doesn't mean you can't then use the daily power of the weapon.
Where this starts to matter is in the regard of, say, Frost weapons. The power says:
All damage dealt by this weapon is cold damage.
Since it's only useable by the item in its regard as a weapon, it only converts damage to cold damage when it's being used as a weapon, i.e. in a power with the Weapon keyword. (Same criteria for when you get the proficiency bonus.)
To further muddy the waters, what about melee implement powers? The DnD XP sorcerer had a feat that allows him to channel ranged attack spells into his dagger and make a melee attack instead.
As long as the power has either the Weapon or Implement keyword, things don't change at all. If, god forbid, it has both the Weapon
and Implement keywords... well, I just don't want to think about how that would work.
Similarly, you can't use a Quick weapon's power from a spell proc, because you didn't use the weapon for that spell - you used the implement.
Good question, though.