I think this is an excellent theory, and a strong possibility that it has happened.
I did some reading earlier. Men who don't qualify for active duty, aka the social service agent, in some cases have the option to choose to serve in active duty anyway. Social service work is 21 months as opposed to the 18 months for active duty, and I find this super interesting. YG had a choice and chose to be there longer, though it does go with many of his old music where he criticizes the mandatory military service. Additionally, social service work is typically done in educational facilities with young children, or working with people who have dementia. Social service workers are bound by a confidentiality agreement, and can't share anything about their work at all, or face jail time. That kind of explains the lack of updates.
What strikes me as odd is, for J!n there were many updates about the quality of his training and behavior during training, without giving specific, but just saying he was a good example. There's no reason why those same type of updates could be made about YG, such as "he works hard" or whatever, without giving away info about the civilians he works with. Afterall, over the years random people have popped up to share stories about YG, saying predominantly favorable things, (probably paid to share these stories to fit a specific narrative), so it is weird for these social service stories to not have been shared yet. Unless there's a legal reason why nobody is saying a word.
Edit: I wanted to add that something like a shoulder surgery, or basically surgery like what YG had, is not something that would disqualify someone from active duty. Physical disabilities that would disqualify someone are being underweight or obese, a significant physical disability in which someone might use a wheelchair or have an amputated limb or deaf, blind, etc., cancer, other health problems that would make service impossible such as heart disease or something like that. For mental health, one of the things listed is obsessive compulsive disorder (OCD). YG is known to have OCD, he even mentions it in the lyrics of The Last. Fans also speculate he has ADHD, and we do know for a fact that he is/was clinically depressed. Prior to the surgery he scored higher, but had less mobility back then, but after the surgery he was disqualified, so I don't think the shoulder is even a factor in how he was disqualified from active duty. Only other thing I can speculate is that he either wasn't diagnosed with OCD before testing for military qualification, OR he was diagnosed prior as his lyrics suggest and it just didn't have enough of an impact on him back then to disqualify him. I should note that disorders grow with a person and change as we get older, so it could be problematic enough today to disqualify him. But again, that's all speculation.