Probably the other way around. Mormonism wasn't founded until the early 1800s, long after the first settlers had arrived in America and "discovered" the Native Americans. The idea that the N.A.'s might be lost Israelites predates Joseph Smith, though he very well may have been influenced by it. It would have made Mormonism a little more convincing to some people if they already had a prior belief in Israelites living in North America.
The idea that the Indians might be a lost tribe of Israel long predates Joseph Smith. It was one of the most common theories pretty much from the time Europeans landed.
Joe just expanded on and elaborated the concept.