Pet Peeve Dept.
“He is tall and muscular, and works out a lot.”
“Works out a lot” cannot stand on its own as a sentence, so it cannot be written as an independent clause as above. The verb “works” is dependent on the prior clause “He is tall and muscular,” using the subject “he” as its own subject. Therefore, “works out a lot” is by definition a dependent clause.
According to the Chicago Manual, a comma should be used between independent clauses but not between an independent one and a dependent one. So, this sentence technically should read
He is tall and muscular, and he works out a lot.
or
He is tall and muscular and works out a lot.
In any event, a strict reading of the OP question renders the answer “certainly not always”. There are countless instances in which a word preceding a conjunction needs no comma after it. Flowers filled the fields, red ones and blue ones and purple and yellow and orange ones.
NO: All dogs, that are not on a leash must be on voice command.
No comma before that coordinating conjunction either. And the list of examples could go on and on and on. 
Thanks to the posters who clarified the logic behind consistent use of the serial comma, regardless of its common omission in American publications. The “I’d like to thank my parents” examples iced it for me. Using the comma cannot create any discernible confusion, while its omission certainly can. This situation is, IMO, similar in a way to the variants listed by Webster’s for the past and present participles of the verb to bus: bused or bussed, busing or bussing. Even though the pronunciations suggested by the morphology of bused and busing are wrong, we already have the words bussed and bussing as the participial forms of the verb to buss (kiss). A sentence such as “My wife and I are strongly opposed to bussing our children” momentarily makes the reader break concentration and seek out clarification from context: What, you don’t kiss your kids?–Oh, you meant putting them on school buses. The tiny instant of confusion is exactly the same as in the “I’d like to thank my parents, Ayn Rand and God” example. It doesn’t take the reader very long to realize the speaker was not parented by Ayn Rand and God, but it’s still too long. Instantaneous clarity makes for smoother reading, which is why from this date forward I am employing the serial comma.