Again, mentioning this only for timeline. In this
SABR article, it says that Jackson signed his first professional contract with an X. I'm guessing the article is referring to Greenville in 1908. This photo is from 1911. So we know definitively that Joe Jackson could not write his name in 1908 and here is a photo with a pretty nice Joe Jackson just 3 years later. In fact, to me this photograph has one of the most fluid and well executed Jacksons of any I've seen, which again must have been signed shortly after he learned to write at all.
I think it's again important to know whether or not Joe Jackson could write his name in 1911. The earliest confirmed signature (on some kind of voucher) listed on PSA's site is from 1916.