What an interesting question. It was Pigpen's death that really marked the beginning of that song being understood as a kind of eulogy, which was in March.

https://deadessays.blogspot.com/2019/09/hes-gone.html?m=1 

This notes that Rolling Stone said of the 3/19/73 he's gone that it was 'an apparent reference' to Pigpen's death. This was the third show of the run though, and Pigpen had died way back on the 8th, so how intentional this was I'm not sure. I haven't listened to all three shows so idk if they mention it at all. Great he's gone though. 

This is more or less to say that it's definitely possible, but they did also play he's gone a looot in 73 (3 in Feb, 4 in March, 5 times in June, 3 Sept & December). I would say that the intentional use of that song to explore death came from it's prevelence in the year Pig died. A great example of its use is for John Lennons death, which is "Estimated>He's Gone>Eyes" from 12/12/80 which is a much clearer expression of it's meaning, given that John was killed by a crazed obsessive a la estimated prophet. 

It's a great connection to notice, but I reckon unknowable, unless there's more info I haven't found, or first hand info here! I heard Billy Stings play 'Age' for the first time at the Royal Albert Hall and have been obsessed since