I'm using the Dropbox iOS SDK and I would like to be able to add a number of files to a queue and upload them to dropbox. I'm using the the Core SDK and I read about a sync mechanism for one of the deprecated SDKs but it does not look like the there is anything comparable for the Core SDK.
That's correct, the deprecated Sync SDK does have offline support, e.g., where it queues up requests, etc. That isn't built in to the Core SDK though, so you'd have to implement that on top of it.