The short answer is no. The log contains a SHA1 commit, which depends on the contents of the commit. If you change the log, you will change the commit, and it will still be invalid.
I wonder why you are trying to do this, really. Inside the vault git logis as good as cat saved-git-log. If you want this to be a change for released versions, just create it as part of the build / deploy process, for example, something like this:
tarname=my-project-$(git describe HEAD).tar
git log > changelog.txt
git archive --format=tar HEAD > $tarname
tar -Af $tarname changelot.txt
gzip $tarname
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