Can a grey shirt sign on national signing day for football?

Someone taking the greyshirt route does not enroll in college until the spring semester. Therefore, in recruiting, he/she wouldn't be considered a true recruit for that year and sign a LOI until the next years signing day. EX: Running back that needs maybe more than one year to physically develop graduates H.S. in May 2008. Greyshirts, so he doesn't attend college till spring 2009. He doesn't sign a LOI until Feb. 2009 and may or may not redshirt in 2009-2010 season. He is then considered a freshman, but still has 5 years of eligibility left (4 that he can play). So his eligibility to play D1 ball doesn't run out until 2013-2014 season rather than 2012-2013.