A priest who used classical pronunciation would be exhibiting an embarrassing affectation. There is in fact an official Vatican pronunciation guide, which I have only seen at the beginning of the Liber Usualis, meaning that the version I have seen is many years old.
However, in Germany they maintain the peculiar custom regarding a soft c which they pronounce like ts and still pronounce magnum as mag-num instead of ma-nyum. Apparently they have always done that and no one objects. Believe, me, and the pope is a great example, German priests who still use it at all know their Latin and pronounce it elegantly, as do the congregations when singing the ordinary, which in Germany is still, well, ordinarily in Latin. I thank my lucky stars that I am both a musician and long ago had the ordinary memorized, and on top of that knew how the Germans pronounce things before I got here. If I only had the churching available in the US in the last 40 years, I would not know what was going on.
I don’t know where the original poster comes from, but I would also not err on the other side of pronouncing the Latin like a typical American priest. I still have memories of priests muttering their way through what we are pleased to call the Traditional Latin Mass without regard for care in pronunciation. In particular the peculiar American way of sounding the consonant “r” makes me shudder when people trying to say something in Latin use it. There was a mentality in the US that it was “sissy” for a priest to strive for a properly continental pronunciation. Besides, it might make the Mass last more than 20 minutes and then people would start to complain.