Short answer - yes. There is benefit in having an understanding of ITIL for a DC Management Role. It depends on the role though. If you are a hands on grunt then not a lot of benefit. If you are the guy responsible for ensuring the SLA's are met then there is a lot of benefit. ITIL is really all about procedures and processes. The Library part comes from the fact that ITIL is based around 'historical best practice', i.e. learn fom your and othe people's mistakes!
The people who really benefit from ITIL are the Project Managers. In general, you will find their advertisements saying things like 'Prince and ITIL knowledge required'.
For me, I've worked in computers for 15 years and in DC's for the last 10, I've done everything from build a DC to being the hands on grunt to being the IT director. I only came across ITIL after I took 6 months off to tour the Far East. When I came back it seemed that ITIL had appeared in every senior job ad.