Premixed ingredients for yogurt
Interesting question. I would certainly say that it's worth a try, because there is a high chance it will work. Of course, you do need to add more culture after cooling, but you already mentioned this in the question. 

If this fails, the most likely failure mode will be that the acid in the culturing yogurt is sufficient, and your milk old enough, that it curdles when heated together. This means that you can either throw it away now, or give it a cook and see if it stays liquid, and if yes, continuing as usual. If it curdles, you can use it as quark. So continuing instead of dumping it is the winning strategy, your worst possible loss is a bit of electricity.