It's worth noting that Beethoven's late piano sonatas did not become part of the public repertoire of pianists until roughly 1860 and were not widely played and understood until the 1920s and 30s. They were first fully recorded (by Schnabel) in the 1930s. That's not to say that Weiss didn't own a score and play Op. 111 privately or with students. Late Beethoven was considered too esoteric and difficult for public performance for a long time. But scores of his works were widely owned and recognized in 19th-century German-speaking culture.
The second thing to remember is that ragtime first, then jazz, were created by African-American musicians from a fusion of multiple influences. Historians and marketing people have sometimes created overly rigid categories that don't capture the reality of music in the Americas. Classical training and knowledge were common among pianists of all backgrounds and used as one part of their language, as I can confirm myself. And jazz did not become a completely separate genre until the 1930s and 40s, when it fully came into its own, distinct from both classical and popular music.
A third thing to keep in mind is that Jewish immigrants were usually less prejudiced and would have had little or no reservation in teaching all kinds of material to a piano student of any race. That this was an issue in the post-Civil War South shouldn't require comment, but take a look at what Dvořák wrote about American music in the 1890s when he visited the US.
While the Op. 111/2nd movement is unlikely to be "the" or even a source of ragtime or boogie-woogie, it is much more likely that both allude to a common genre, the marching band and its relative, the waltz, the most common kind of syncopated style in nineteenth-century music and one source of syncopation in popular music. And marches do occur in Beethoven in many places (Op. 101/2 (scherzo, alla marcia), more famously in the Third Symphony and Ninth Symphony, with the miniature oompa band in the final movement.
I'm listening to Op. 111 right now, and I've played it in the past -- Beethoven arrives at something like boogie-woogie by progressively more subdivisions and syncopation that starts with something like a minuet, then a waltz or a scherzo (in 3/4, but faster still with only one real beat: ONE-two-three). And while most often 2/2 or 4/4, march time can be 6/8, a spritely relative to the waltz 3/4 -- Joplin would certainly been familiar with these styles and genres. Beethoven's triple 12/32 time is a subdivision of 6x2/8x2x2 (with the extra 2s reflecting Beethoven's finer and finer subdivisions in the sequence of variations, and you can factor this signature more completely).