I was thinking about that a few months ago, I was debating with some friends about it and we was discussing about if we will see Tumbleweed before it did get deserted, and we was also trying to find info about a possible date for when the town did get deserted.
The wiki for Tumbleweed is the best place to try and find out when the town last had been occupated.
http://reddead.wikia.com/wiki/Tumbleweed
The only dates to go by are what are marked on the graves at the church in Tumbleweed, the latest date recorded on the grave stones was 1906, 5 years before the events of RDR 1, so there is a possibility of seeing Tumbleweed before it got haunted and deserted.