Only if you assume that the Forgotten Realms setting is inexorably connected to Planescape.
You can always think of Planescape as its own setting. I guess it depends on how you played: did you frequently bring your FR or Ravenloft or whatever characters from their campaigns for a visit to Planescape, only to return to their original homes and continue the status quo? Or did you roll Planescape-specific characters, and used it as a hub to hop from setting to setting, and then go back to Sigil for another tour later?
In the first case, I agree it could be a problem, although Sigil still exists in the new Cosmology BTW, you just now have different planes to visit. In the second case, you'd have to think, who cares if you visit Greyhawk or Dragonlance or whatever? And if the point of Planescape was to connect other settings, it was kinda doomed from the start, since it depends on every one of those universes remain unchanged and interconnected.
Now that I think about it, I don't see exactly why Planescape can't exist in the new setting with all the changes. It just also needs to change (think something else to replace stuff like "the Big Devil vs Demon Superbowl").
In fact, by its very own nature, Planescape joins several otherwise completely different settings, and if any change in any of them is going to break Planescape, then it was doomed from the start.