If you had discouraged them from getting together they would have remained friends but not developed a romantic relationship.
The pivotal sequence for the Joker-EDI romance relationship occurs after Priority:Citadel 2. When you encounter Joker in the bar you have a final chance to discourage the relationship.
If you do then they will not then if Joker survives the crash of the Normandy in the final sequences (eg if you have a high enough EMS) then EDI will not accompany him.
I had read this a few days ago while looking for other information and it's mostly confirmed by the Mass Effect Wiki.