It should probably be pretty trivial to roll together a TimestampMod equivalent using a similar methodology as git-notes. Hell, just store a git-note for every commit in a non-standard ref; each note would have a printout of the tree and corresponding timestamps. To reapply timestamps, you'd just have touch run through the git note, re-touching every file to have the appropriate timestamps.
Like others have said though, I don't understand what a use case for this would be. The page for that Hg plugin seems to indicate that it is just meant to ease the transition to version control, for users who don't yet 'get it'.
I'm really curious about your use-case. Are you just looking to tweak the behavior of the VCS w.r.t. a timestamp-sensitive build system?
I will say that file timestamps invoke horrible, horrible memories of an employer that used Visual Source[un-]Safe -- a VCS that relied on accurate client system time for history integrity. I.e. the repo was easily corrupted if a client wasn't on synchronized time. Also, race conditions. AFAICT, it met none of the conditions casually denoted by the words "Version Control System".
I'm curious why you need to preserve the timestamps. I'm not saying it doesn't make sense, I just haven't ever had a time where that's been a requirement.