If everything in the universe is slowly drifting away how soon before we see signs of this?Maybe we’ve already registered things at the visible edge of the universe disappearing. If not will, it ever be possible?
Wikipedia's article on the Observable Universe give an answer for this question.
As the universe's expansion is accelerating, all currently observable objects will eventually appear to freeze in time, while emitting progressively redder and fainter light. For instance, objects with the current redshift z from 5 to 10 will remain observable for no more than 4–6 billion years. In addition, light emitted by objects currently situated beyond a certain comoving distance (currently about 19 billion parsecs) will never reach Earth.
So yes, we will eventually (in fact already are) seeing things disappearing.