Can most native speakers of a non-Tokyo-type pitch accent pattern “correct” their pitch when they speak 標準語?

For the more advanced learners, linguists and any natives, if on here.

We know that almost all educated speakers learn standard Japanese in school and are able to produce it easily both orally and in writing. Even if they might usually use their own 方言 with friends and family.

My question is, are they also able to switch to the Tokyo-type standard pitch pattern when they speak 標準語? Or would they still use their dialect's pattern, but standard grammar/vocabulary?

I started to wonder because while I can often hear the different pitch pattern in (for example) anime characters with a strong 方言, I don't often hear it when natives speak the standard dialect. That is, I cannot really distinguish accents in Japanese, unless they're actually using features from their dialect. So I started to wonder if they are actually almost all adjusting their pitch when they speak standard or it's simply that I can't hear it very well.

When it comes to dubbing, I also wonder if many dubbers who are from Tokyo are actually putting on a dialect for the purpose of the character, but fail to reproduce the same pitch pattern for that dialect.