Did tariffs boost 19th century U.S. economic growth?

It is a common view that the growth experience of the United States represents a strong case for the "infant industry" argument for protection.  Bill Lazonick told us this repeatedly in my Harvard history of thought class.  But is it true?  Via Ben Muse, Douglas Irwin says no:

Were high import tariffs somehow related to the strong U.S. economic growth during the late nineteenth century? One paper investigates the multiple channels by which tariffs could have promoted growth during this period. I found that 1) late nineteenth century growth hinged more on population expansion and capital accumulation than on productivity growth; 2) tariffs may have discouraged capital accumulation by raising the price of imported capital goods; and 3) productivity growth was most rapid in non-traded sectors (such as utilities and services) whose performance was not directly related to the tariff.