False.
The War of 1812 did not delay the completion of the first section of the National Road, as construction on the road did not begin until 1811. The first section of the road, which ran from Cumberland, Maryland to Wheeling, Virginia (now West Virginia), was completed in 1818. However, the war did have an impact on the funding and construction of the road in subsequent years, as the government had other priorities during and immediately after the war.