By design, EAMs are sent out via redundant communications systems, wireline & RF, but it doesn't really matter how an EAM is received, as long as it's properly formatted, decoded & authenticated. Primary EAM distribution systems have to be certified by the JCS in terms of their reliability & speed, and while SATCOM has been in use for a long time, it wasn't necessarily considered to be a primary EAM distribution method until towards the end of the Cold War when the high-tech SATCOM systems were deemed reliable enough.
Best way to research the use of SATCOM for EWO/EAM stuff is to examine the comms capabilities of the strategic nuclear forces -- bombers, missile alert facilities, & SSBNs. All have had UHF SATCOM capability --at least receive-- for decades. Specifically, the B-52s & even FB-111s as well as Minuteman ICBM launch control capsules had AFSATCOM terminals for receiving SAC 'Giant Star' data traffic (mostly 244MHz), while ideally also receiving it via HF voice & the Survivable Low Frequency Communications System as well as several voice/data mode wire-based systems.
The SATCOM systems for the Minuteman force was greatly improved, first with a 'soft' SHF-based system (that, & other redundant comm systems caused them to stop using HF/SSB at most Minuteman sites) & now a hardened EHF system. The B-2s also have have EHF capability long enough to where it's now being upgraded & you'll notice you don't see any bulbous antenna like you do on the E-4B or E-6B aircraft.
The communications teams that travel with the National Command Authorities use SATCOM extensively when mobile or out in the field secure Iridium or Inmarsat, secure UHF satcom, and secure EHF terminals for primary voice connectivity & access to things like the Global Information Grid & specialized NCA/MEECN stuff.
I am the King of All Monitoring.