Projection Position idenmpotency on Deletion and recreation

Currently we have a number of worker services reading the $all subscription to create view models etc.

Looking ahead we hope to move to subscribing to more specific projections. As our workers process each event, they persist the event position (which for $all is nnnn,nnn, and which changes to a single number when reading from a projection stream). This allows us to track where the worker last got to (So it can restart etc). If there is an issue with, or we need to delete the projection and recreate it with the same or a different name, will that last position still be guaranteed to point to the correct event?