It should work OK. When you start LRCC after re-installing it, it will automatically rebuild your local library from the cloud, but as you've already realised you'll need to then change the preferences to opt for originals to be stored locally, and the location to be the same as previously set. LRCC should then find the originals are already in the specified location and simply update the records for each image to show that the original is now stored locally.
I have done a brief test, and that seemed to work OK, but no guarantees.....worst case scenario if it doesn't work is that you'll have to delete the first set of originals and wait for the new set to be downloaded.
Thank you. I will try and let you know.
Don't worry I have (too many) backups, so as to guarantees, I believe that the only things guaranteed in life are death and taxes!
This worked perfectly. The files reconnected and there were no duplicates.