I wouldn't use it that way, but my dictionary lists meaning number four as "to dedicate to some service or goal." Still, I don't think "memory" would fit that definition. I think Abe said "we have come to dedicate a portion of that field to those who here gave their lives etc.", if memory serves me correctly. So "dedicated to the memory" would work.
It's fine. Here's an example: The American Memorial Chapel at the very east end of the church in the apse is consecrated to the memory of over 28,000 US servicemen based in Britain who died in the Second World War.