I'm not really sure there is such a thing as a no risk medication. The two active ingredients of Thornit's, iodoform and boric acid, are certainly toxic in dogs if taken in excess.The lethal dose for iodoform is high at 1000mg/kg, but it does have toxic effects on liver cells and other systems at much lower doses.
"Iodism has been known to result from continued or extensive application of iodoform to wounded surfaces; dogs and cats are said to be particularly susceptible to this form. Poisoning in these species is characterized by vomiting, muscular spasms, a lowered temp, cardiac depression, and drowsiness.
[Clarke, M. L., D. G. Harvey and D. J. Humphreys. Veterinary Toxicology. 2nd ed. London: Bailliere Tindall, 1981., p. 54] **PEER REVIEWED** "
If Thornit's powder is applied to to paws and other areas of the skin it is certain to be licked and therefore ingested by the dog as well as being absorbed through the skin. At least that is not going to happen when it is used in the ear. Although practically, the dose of iodoform and boric acid is likely to be be small if used sparingly and for a short time, people should be aware that these ingredients are toxic. That's one of the reasons I get so annoyed with statements like the one on the Thornit's web site that says: "There are no antibiotics in THORNIT, so it can be used in perfect safety." Are antibiotics really the only dangerous thing you can give an animal?
As to whether it's a good idea use Thornit's to treat for mites just in case, the OP has said that the vet put the dog on Advocate which controls ear mites. I would follow the vet's treatment plan and let the Advocate do its job and treat the dog for yeast infection with shampoo as prescribed.