I don't think we have a connection, given the information you said, but here is our information for you to evaluate. My relevant Ancestry.com tree is named "Skocpol/Sadilek/Jurka". I hope that you can see it, if you want to.
My great great grandfather was Frank J. Sadilek (1851-1933), Frantisek = Frank. He was born in Ledec nad Sazavou, came to Chicago in 1868, then Omaha and soon to Wilber Nebraska. He had a son Frank J. (1882-1973) born in Wilber, and that Frank J. had another Frank J born in 1907 in Omaha (of whom little is known). The original Frank J had a brother Karel (Charles) (1857-1936). Those are the only boys in that generation.
Their father Jan Sadilek (1817-1882) was also born in Ledec n.S. He also came to Chicago in 1868 on a different ship, but stayed in Chicago, until going to Wilber in 1880. He and his wife had two daughters (Frantiska and Marie) and two sons (Frank and Charles), all of whom came to the USA. Three other children died in their youth. Jan Sadilek had a married sister, who lived in Chicago before any of them did. Her married name would not be Sadilek. Thus all of my Jan Sadilek's descendants are accounted for in the US. Jan's son Frank (my great great grandfather did not mention in his published reminiscences any other uncles or aunts who remained in Ledec.
His father Jan Nepomucky Sadilek (1790-?) was born in Ledec (#12), and Jan N.'s father Josef Sadilek (1755-1816) was born in Cervene Janovice, Central Bohemia but died in Ledec. We have no information about whether they had brothers that could continue the Sadilek name.
Your grandfather Jan was born in 1905 at Ledec, and had a "great uncle" in the US.
A great uncle would be born two generations before 1905. Two generations could be 30 to 80 years (at the estimated biological extremes). That would make the "great uncle" born between 1825 and 1875. Are you meaning to say 1) that your Jan's great uncle's name was Frantisek Sadilek (born between 1825 and 1875), or 2) that your Jan's father (one generation back, 15-40 years, born in 1865-1890) was named "Frantisek Sadilek"?
Based on my estimates applied to case 1), my great great grandfather Frantisek (Frank) born 1851 falls in the right range. He could be the great uncle. But for the strict meaning of "great uncle", Frank would have to have a brother left back in Ledec, to become your Jan's grandfather. I am sure that our family would know about that. (They visited relatives in Bohemia in 1910 and 1920, and my great grandmother Dr. Olga Sadilek Stastny, M.D. worked there 1919-1921.) With a looser definition of "great uncle" such as "great-great uncle" there could be unknown siblings of earlier generations starting other lines of descent. As for case 2), Our Frank is the son of Jan, not the other way around.