Touring on a Tri bike?
It depends entirely on what your are trying to accomplish and what your expectations are.  Many RAAM riders opt for a TT style setup, so don't let the long distance dissuade based on "it's not done" that way, because it is (by some riders).  

A large consideration may be parts and maintenance.  Most traditional touring bikes opt for simpler parts that are easy to repair or find replacements for.  I saw a guy attempt a similar thing on a TT bike starting up north on the Haul Road and planning to finish in South America.  He crashed soon into his ride and needed a new derailleur hanger and bar end shifter for his fancy bike.  Since the hanger wasn't available in town (direct from manufacturer part) our mechanic had to fabricate him a hanger out of scrap.  For the shifter, nothing (within reasonable expense) could be done.  He was forced to call ahead to a shop in Canada and hope they could get one ordered and available by the time he got there, then ride without it for several hundred miles.  

Also, from commentary from links on another answer, tire selection may be impacted.  Depending on the rear tolerances on your TT bike, your selection of tires may be limited to less than desirable tires for touring.

The point being that TT bikes tend toward extreme specialization and part styles that aren't often carried in stock.  As long as you are aware, careful, bring your own second TT bike, or comfortable with the possible delays (or some combination of the 4) it may be fine.