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.

![EDI-blocked][1]

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.


  [1]: https://i.sstatic.net/bKYX2.jpg