"Greatly" is relative. The PA state archives has a selection of daily symbol freight summaries for the PRR during WWII that includes counts of oil trains and how many oil cars passed through Pittsburgh for points east:
5/1/43 - 884 cars in 13 trains
Article says pipeline completed to the east coast October 1943.
11/30/43 - 326 cars in 5 trains
5/6/45 - 215 cars in 3 trains
What I don't know is whether demand had grown so much that it exceeded pipeline capacity, or if some east coast refineries were not reachable using the "little-inch" pipeline.
I am in Lewistown, PA today along that same PRR mainline, and sadly several oil trains have passed today.... With a tonnage that probably exceeds the 11/30/43 total...