I have an omega 36m I believe it has a titanium outer tube and stainless steel baffles.  Would it be safe to throw it in the ultrasonic cleaner with power purple like I do for my rimfire baffles?

Yes.  But I can't guarantee it won't compromise the paint on it.

The omega 36m is known for it terrible finish and I have got it hot enough most of the finish is gone anyways.

36M is cerakoted.  It depends on which cerakote series was used on it.  The baked on 2-part H series is a bad choice for high heat applications as it's only rated to 500 degrees.  The C series air dry stuff is rated to 1200 degrees without discoloring, but it's not as durable to abrasion, chipping, etc.  V series is a 1-part (no hardener needed), but does require baking at 500 degrees and once cured can handle up to 1800 degrees.  

Unfortunately, as you go into the various higher temp series, color choices become limited as well.

As for titanium itself, yes, perfectly safe in an ultrasonic cleaner.  Cerakote SHOULD be OK, but that might depend on the chemicals/cleaning agents you use.  Also, if it has any chips or cracks in the cerakote, it might cause more chipping.