Yes, you can use a single auxiliary:
"I shall arise and go now;"
"But thy eternal summer shall not fade nor lose possession of that fair thou owest."
If Yeats and Shakespeare can do it, you can too.
However, I do not find either of your sentences to be flawless.
"One who speaks articulately will be both appreciated and known as an expert in English."
There is no need to separate the subject from the verb with a comma. And it is clearer to be explicit that the field of expertise is the English language without any possibility of implying that the expert is of English nationality.
"One who speaks articulately will both be appreciated and be known as an expert in English."
This addresses the same issues as in your first sentence, but gets "both ... and" parallel in the forms being paired.