While Beethoven was indeed a genius as far as music is concerned, it is very much understandable to think that his study of earlier classical music wouldn't have made any difference if he had not studied it although we cannot totally conclude that it didn't have any impact on his career during his late period. It is on record that Beethoven started composing songs when he was still young.
And most of his songs in his early period were meant for public consumption. To me, I think his knowledge of earlier classical music had a huge impact on his late symphonies. If you critically study Beethoven's life, you will see that he gave himself to different musical pieces of training at each stage of his life. However, it is important to note that Beethoven didn't release more symphonies on classical music in his late period, because he worked more like a romantic composer.
I do not believe that the early Classical education played into the later symphonies written by Beethoven. While he studied under the greats, he took his musical ambition in a new direction, entirely his own. The ingenuity showed by Beethoven could have been achieved without studying under the great composers. He would have heard their music, and been able to take what he needed to produce the amazing pieces that he did.
Given that he did not care for much of the social niceties of the day, and was known to have a rather terrible temper, it is impressive that he managed to study under anyone for a length of time. Beethoven was a musical genius and one that deserves the continued celebration that he receives today. Many of the pieces that he composed received scathing reviews from some of the noted musicians of the day, but they have stood the test of time to become among the most played pieces for concerts, weddings, and more.