Is this actually a plausible sentence?

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Seems plausible to me, which part are you doubting at?

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imo a better translation would be,

“don’t say anything, shut up, and leave” (for me)

It is not easy to translate the くれる and 丁寧語 aspect of this sentence into a single sentence in English.

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Yes, this is a plausible sentence. All of the sentences on the site are written by native speakers. In many cases, くれる can be used sarcastically to mean ‘Why don’t you do me a favor and ~’. In this case, it means ‘Why don’t you do me a favor and shut the heck up and leave’.