You should be fine if you implement the data source methods related to sections.
For example:
- numberOfSectionsInTableView
- sectionIndexTitlesForTableView.
Any time the table data is reloaded (e.g., [self.tableView reloadData]), these methods will be called and the data will be placed into their sections.
Keep in mind that the cells are just the visual representation of your model, which in this case is your fetched data. The cells are not assigned to sections; they are simply created however you specify for your model (via the table view data source and delegate methods).
Regarding deletion of entries while using Core Data, I suggest taking a look at NSFetchedResultsController. The latter will monitor any changes to your table's data and message its delegate, your table view controller, when updates are made.
For example, a deletion would start with a call to the table view delegate like normal (i.e., via tableView:didEndEditingRowAtIndexPath). Within the latter, you would then delete the entry from core data (e.g., [self.myDatabase.managedObjectContext deleteObject:entity]). Assuming you initiated the NSFetchedResultsController w/ the same managed object context, the deletion would be automatically reflected back to your user.
If you're using a remote DB, however, you'll also have to perform a save (however you've implemented that) to ensure the DB is updated too.
Note also that if you use an NSFetchedResultsController, you don't need to implement the section data source methods since NSFetchedResultsController can handle that for you. Just define the key-path in your data model that will return the section name when initializing the NSFetchedResultsController.