Hi Chris
So this is a mass produced low end beginners banjo, Not what I thought it might have been which looks more like this. This is a banjo that uses goat skin or vellum, held on with a tension hoop. This is how banjos used to look like before the Remo plastic heads became popular. This design dates back to the 1900’s or earlier.

As @BanjoBen has said already - quote “Probably not, as the rim has to be cut so that the tone ring can fit on it.”
That said however, there are folks out there that do luthiering as a hobby and maybe they have figured out a way to add a tone ring to improve the sound on these low end economy instruments.
Head over to the Banjo Hangout and post your query in this link. Be sure to include the pictures and I am sure you will get a quick response.
https://www.banjohangout.org/gotoforum/12