I have a friend who has drag raced a Hondamatic for years. He leans on the motors pretty hard, but leaves the transmissions alone. He and another acquaintance who is a former Honda mechanic both claim the transmissions are indestructible. I guess you could tear one up, but due to the fact that they don't shift automatically, they hold up pretty good. Shifting (slow or soft) is what hurts automatics in cars and trucks. A good quick clean shift reduces wear on the clutches and bands. The Hondamatics have a nice shift IMHO.
I could see a side car adding some stress (heat in the converter) taking off, but once underway things should run as normal.
FWIW, my Hondamatic is the only automatic transmission in our daily fleet. The truck, wife's car and my 4-4-2 are all manuals. How ironic is that?