Additive phrases and usage of Comma

Dear sa2222,
I'm happy to respond.

First of all, I will say that far more important that anything about commas are the rules concerning the definite article. You absolutely need the definite article in front of the two people-related nouns in this sentence --- not "secretary" but "the secretary"; not "mayor" but "the mayor." Any noun referring to a specific office absolutely has to have a definite article if we are referring to a particular person. If we are speaking in general, about no person in particular, perhaps hypothetically, we might say "a mayor of a large city might be ..." --- in other words, we might use the indefinite article under certain circumstances, or another modifier, but the unmodified word "mayor" with no article of any kind is NEVER used.

The rules about use of the definite article are very hard, and much much more important than rules about commas.

Now, as to your question --- think about it this way. Additive phrases that begin with "as well as", "in addition to", "including", etc. are noun modifiers. The general rules for commas around modifiers has to do with the distinction of vital vs. non-vital modifiers. See:
https://magoosh.com/gmat/2012/gmat-gramm ... modifiers/
I would say that, most of the time, additive phrases are not vital noun modifiers necessary to establish the identity of the noun; by their very nature, additive phrases are "extra," adding something else that is not necessary to the original noun. That would imply that, in the vast majority of cases, the additive phrase would be set off by commas.
The secretary, as well as the mayor, is joining the party.

Does this make sense?
Mike