Use rsync's checksums to deduplicate across backups

[Alex Waite]

    I apologize if this has already been discussed before, but as of
yet I have been unable to find any info on the topic.
    I have a very simple (and common) disk based backup system using
rsync, hard links, and a little bit of perl to glue it together.
Remote machines are backed up regularly using hardlinks across each
snapshot to reduce disk usage.
    Recently I learned that rsync does a checksum of every file
transferred.  I thought it might be interesting to record the path and
checksum of each file in a table.  On future backups, the checksum of
a file being backed up could be looked up in the table.  If there's a
matching checksum, a hard link will be created to the match instead of
storing a new copy.  This means that the use of hard link won't be
limited to just the immediately preceding snapshot (as is the case
with my current setup).  Instead a hard link could be created to an
identical file located in a different machine's snapshot.
    My initial concerns were that doing the checksums would be too CPU
expensive, but if rsync is already doing them then that isn't a
concern.  My next thought was that the checksums would be susceptible
to collisions, thus leading to potential data loss by linking to a
non-identical file.  However, from what I've read on wikipedia, rsync
does both a MD5 and a rolling checksum.  These two together make it
/very/ unlikely to have a collision, thus accidentally linking to a
non-identical file is unlikely.
    Is this approach even possible, or am I missing something?  I know
my labs have a lot of duplicate data across many machines, so this
could save me hundreds of GiBs, maybe even a TiB or two.
    If this is possible, how can I save the resulting checksum of a
file from rsync?
   Thank you for your time.  I look forward to hearing your thoughts.

---Alex