Aside from providing workers to build the infrastructure of American transportation, the huge influx of immigrants also created a need for that means of transportation. Immigrants who moved to the U.S., particularly the Irisn as well as Poles, Russians, Lithuanians, etc. tended to settle in big cities, and often lived some distance away from the factories in which they worked. Because of this, it was necessary to develop a localized transportation system of street cars, trains, etc. to transport people to work. These people also were consumers of goods produced in America's heartland, and therefore contributed to the demand for meat, grain products, etc. produced in areas far distant from the large cities.
It is an elemental fact of economics that one must have demand before there can be supply. While immigrant labor helped build much of the nations infrastructure (Irish worked on the Erie Canal and Chinese workers on the trans-continental railroad) a substantial portion of the demand for transportation resulted from the large influx of immigrants during the 19th century.
The main way that immigration affected transportation in the United States was by providing the workers who were needed to create some of the most important infrastructure of the 19th century. The major example of this is the railroads. Many of the people who built the transcontinental railroad were immigrants. Immigrants who came to the US from Ireland worked on the railroad from the east while many of the workers in the west came to the US from China. By providing labor to make the railroads (and, earlier, canals) immigrants affected America's transportation network.