Indeed they can. There was a player last year at my son's school who decided he did not want to wait his turn and he requested a redshirt from the coaches and he got it. That opened up a roster position for my son who was up to that time a redshirt.
JR, Redshirting is no longer permissable in DIII, other than for very limited medical reasons. I believe this ruling became effective for the 2005/2006 school/athletic year.
By a VERY slim vote last year, NCAA D-III's voted to allow D-I and D-II players that transfer to D-III's to have the benefit of the redshirt they wore at their original D-I or D-II. Not sure if this will last once you get beyond exisiting players that transferred from D-I's and D-II's before the D-III redshirt was canned.
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