Can a half-elf from a class that does not use any implements use his dilettante racial trait to choose an at-will power with the implement keyword? At higher levels, would that allow him to use an implement with a magical bonus, or is he stuck at using that power with no enhancement bonus?
Half Elf Dilettante does not grant any implement proficiency. You can still use the power (unless a specific implement is required). But, no, you can't use enhancement bonuses from magic implements at higher levels either.
However, most implement powers can be used with any implement, and thus if you are part of an implement wielding class already, you do not generally need a special implement for your dilettante power.