@Echo4Thirty
I know this is a bit of a delayed answer, but you or other folks may find this useful. At work we use quite a lot of Iridium PTT equipment (Icom Sat100 and Sat100M) globally. I have working with Iridium engineer a few times and try to pry as many details out of them any time I can (the inner geek in me wants to know). So here are a bunch of geeky details...
To answer your main question, I don’t think Iridium PTT traffic is true VOIP traffic that you would think of from a networking perspective. Just based on my experience using various Iridium services, I believe the PTT voice stream is a modified version of their sat phone voice protocol (don’t take my word as gospel on this).
For commercial customers, a PTT call involves any of the satellite in view of the user devices in questions and servers at the Iridium commercial teleport in AZ. When a PTT radio keys up, it sends its GPS location and the TG ID number of the channel it is trying to access. That request routes up to the satellite, then to the AZ Iridium teleport, is processed by their servers (they call it a GBC= Global Broadcast Controller) where it takes the user's talkgroup locations, memberships, and then replicates what is transmitted and sends it to the targeted broadcast areas to the authorized users per the settings in the PTT Command Center.
It is frustrating that Iridium has not developed any direct IP/ROIP connection from there network to the outside world. This prevents any real system to system interoperability development. Any interoperability has to happen at the end user device side. Iridium holds a view similar to other satellite owners that they maintain the transport network and development of features for the end users are the responsibility of the equipment manufacture. I have been pretty impressed with Icom’s Iridium radios. It seems like they have put a lot of thought of what radio features they can implement with the limitations Iridium hands them. For example the Sat100M (base station model) actually puts the antenna and RF module in the external antenna and then connects the base unit and the antenna via a ethernet POE connection. No need to run large coax cables to the antenna on distant runs.
You are right, the Sat100 radios (portable units) can only talk via Iridium. No Wifi or LTE probably because there is no way to backhaul the traffic back to the Iridium system. Icom announced last year they were developing a new version of the Sat100 radio that would also incorporate an LMR radio into the handset. I hope this ends up being a tight integration between the Iridium network and the LMR system (like how some of the P25 radios can ‘roam’ between LMR and LTE). This would be much better than just stuffing two radios into the same handheld.
One note. While not directly applicable in your situation, Icom offers the VE-PG4 radio gateway. Along with typical radio gateway stuff where radios are connected to the gateway via audio cables, the Sat100M radios can be connected to the radio gateway via IP network. We use this in a few locations to connect our VHF repeater system to a Iridium PTT talkgroup.
Hope this helps or is at least interesting to the next person.