There is the example of the 37th Squadron in the Caldari Navy which is comprised of capsuleers who use T2 ships in their standard org chart:
"As of YC119, the 37th (Octopus) Squadron’s seven flights are organized as follows:
Gold Flight - Command Operations / 5 Battleships (Rokh and Scorpion)
Silver Flight - Bombardment / 5 Battleships (Raven)
Weird Flight - Electronic Warfare / 3 Frigates & 3 Cruisers (Kitsune and Blackbird)
Orange Flight - Heavy Assault / 5 Cruisers (Cerberus)
Red Flight - Light Assault / 5 Cruisers (Caracal)
Blue Flight - Rapid Attack / 5 Frigates (Hookbill)
Green Flight - Rapid Support / 5 Frigates (Griffin and Kirin)"[1]
Emphasis mine.
The 37th is just one capsuleer squadron within the Caldari Navy and one of many specialist squadrons.
The important distinction to make however I think is that if you are a military capsuleer or work as part of official government forces you would already be doing so already.
As to why people decide to go freelancer and independent and then turn around and try to tell people they’re actually serving as part of the actual armed or government forces is really anyone’s guess though.