False. Being able to laugh off Mesopotamia things was BEFORE she dropped down the underworld. And Quetz, Gorgon's damage were minor despite going all out, with Gorgon dying. They could only stop her from flying up the sky. There's a reason Gramps only show up when she is already down the underworld, being shut out of her protection. Merlin was there to neutralize the mud so she cannot regenerate back all of her wounds, not damaging her. And even with all of that stuff, they were still unable to destroy her servant-level saint graph without Gil's help. The actual pain train was only possible after underworld drop AND Death concept. None of this would be possible for Surtr, for yet again the Yth time.
Also the logic "only effective to things within your myth"
would also apply to Surtr. He might be good for the Norse texture, but when the foreign kaiju comes in, that's when the pain train will start for him.