Very young M. pudica ("sensitive") plants may not have thorns, but other than that, yes - M. pudica will have thorns. The movement is apparently more noticeable on them than the Florida native M. strigillosa ("Sunshine" or "powderpuff"). M. pudica does not form a mat-like groundcover like M. strigillosa does, and instead grows more shrublike, although it will not form a dense shrub appearance. It's usually grown as an indoors container plant for curiosity value, but has been found growing in weedy areas in the Gulf states. M. strigillosa spreads out in a mat; it will not grow "up".