Was immigration during 1830s to 1840s vital to the industrialization of america?

In general, yes, immigration during 1830s to 1840s was vital to the industrialization of America, since it was mostly immigrants who first sought employment in the factories that were an essential element of industrialization.

Cherokee  removal, part of the trail of tears, refers to the  forced  relocation between 1836 and 1839 of thecherokee  nation from  their lands ingeorgia, south carolina, north carolina, tennessee, texas, and alabama to the indian territory (present day oklahoma)  in  the thenwestern united states, and the resultant deaths