It would take as much time as it currently does to do a remote -> local sync. The slow part is recursively parsing every remote folder to see the current contents. Normally when syncing remotely to locally there aren't that many files changed. It is usually that a user has a large folder structure, or a connection that is no super-fast that causes it to be slow process.
For users that want to work on remote files as if they were local, with the full functionality of Sublime, you should try out expandrive.com. Some users find it fast enough, other find it too laggy.
The way to get the absolute best performance of working on remote files as if they were local is to make a local copy and use rsync to copy down the latest changes. This requires that the user have SSH access to the box and the rsync program installed locally and remotely. This can very efficiently detect the differences between files and it only transfers the data necessary to synchronize the two copies. There is still the limitation that you need to rsync pretty frequently if other users are also modifying the files.
Eventually people tend come to the conclusion that using a version control system is the best way to handle multiple people working on the same files, and ensuring that data is not lost. Unfortunately this is not always feasible based on project constraints.