Yes a skinny person, or at least a relatively skinny person, can make it in the NFL. While size does matter for some things, in football the most important aspect of any NFL player, regardless of size is fitness. Can you imagine a 350 pound lineman with his huge hulking legs trying to kick a field goal or run a down and out pattern like the “skinny” wide receivers?
Corner backs have to be relatively skinny too in order to keep up with the speed of the wide receivers and tight ends. And, special teams’ players can be skinny guys too.