After a quick look at census records ect, it looks like our best bet for a tidbit of any trip to Chicago area might have to come from his obituary.
William Walter Phillipi appears on the 1900 through 1930 census in Cass County. He has the required WW1 registration and also a required WW2. He is also listed in the 1917 Farmers Directory. On the surface it appears William never left Cass Co nor did he ever marry (at least pre 1930). He lived 1920-1930 with his single brother/sisters and their mother's sister (who died in 1939 at age 102).
William born 30 Nov 1887, died 28 March 1969 and is buried in Beardstown City Cemetery, Cass Co IL.
It also might be easier to try and confirm or rule out why you think this William Philippi was in Chicago during the times of 1908-1913. Is there a chance you're confusing him with a different William Philippi? Again, based only on a quick look, it appears on the surface that the Cass Co IL William Philippi lived as a farmer and as a single gentleman (at least from birth through 1930)...there is always a chance this one could have took a trip and/or visited the Chicago area, but a search of the newspapers for a 4 or 5 yr period looking for a brief mention of a trip/visit is something I would imagine you'd have to try and view daily/weekly newspapers via film to try and verfiy, a time consuming effort. Could there be a mention of his whereabouts in his father's obit of 1912 or his mother's in 1908?