Can Ultherapy accelerate long-term aging if you do it in your 20's by damaging tissue and architecture of skin?

Goodness, NO!! The opposite is true!! Ultherapy causes a tightening of the skin by inducing a tighter coiling of the collagen, and stimulating fibroblasts to produce new and more collagen and elastin by increasing the temperature of the target tissue (deep dermis) to 68-70 degrees Celcius, without increasing the temperature of the surface of the skin so dramatically.  It can also shrink the SMAS, the target tissue of facelifts and necklifts, and is the only FDA-approved device capable of giving a non-surgical facelift or necklift.  So with those two actions, it is basically making your tissue more like it was when you were younger, and not altering it into an unnatural form.  The only way I can logically conceive that a person might get an undesirable aging effect from Ultherapy is if there was treatment to the skin's fat layer in an area you do not want to lose fat as you age...such as the cheeks.  
Telomeres (on the ends of chromosome chains) are not a target tissue of Ultherapy.  The mechanism of action of Ultherapy is to have radiowave sources of a specified energy collide at a predetermined depth from the (transducer) source, producing microfocused energy that results in shrinking the target tissue, be it deep dermis, subcutaneous fat, or SMAS.  
I applaud your thinking through long-term consequences of cosmetic procedures. In the case of Ultherapy, I believe that ultrasound technology has been around and used for generations, and is quite safe when used as intended.