Hi Martha,
I never got any answer here, but I can tell you what I found out since I posted this.
Short answer: FieldMaps/Collector in and of itself has no support for post-processing; any correction must be done in real time with either SBAS or an internet-based correction.
Long answer:
There is a half-exception to this: Using Leica's own software (Zeno Mobile and Office), coupled with one of their receivers, you can post-process hosted Feature Classes in place (meaning no copies will be made, the actual data will be corrected) provided they were collected with the Leica Mobile app. (Their workflow also allows for post-processing in ArcMap, but that requires you to export the entire dataset as a copy, so you can't do it in bursts.)
Post-processing is available as well if you have Trimble Terraflex/Positions (Terraflex is for collection, Positions is for post-processing-- it's an evolution of Trimble Pathfinder Office), which again requires ArcMap at this time to use. The workflow is kind of arcane to get started on, but overall it's a decent data collection app (Nested collection!!!), and the post-processing is good. It also lets you do it piece-meal; so you can export features every day if you want, and correct multiple times, even re-correcting the data if needed.
Barring those two options:
(I mention this because access to our Enterprise server is only available on our office wifi/Ethernet connection)
If you have an iPhone (or an iPad with a data plan) and you have service where you're collecting data, you can go to the Settings and turn off data access to FieldMaps/Collector, but use the data connection to real-time correct. This is not natively supported in Androids, but can be done with a third-party app of some sort.
I really, really wish FieldMaps had post-processing functionality.
Hope this helps!
