@G. Tomevi: Taken alone, "So does coffee." is incomplete, yes. But since it follows a sentence which contains THE complete thought, it becomes complete. Sentences of this construction should normally follow a sentence which contains the complete thought, or part of the whole context. In this case, "Tea has caffeine." does the job of providing the complete thought.
@Roaring Fish: This is the part of the original post which contains "does."
"...so does coffee."
Not only is this clause emphatic but it is also inverted (the verb does precedes the subject coffee). Moreover, this second clause follows an independent clause (Tea has caffeine) from which it takes meaning to complete the thought.
To construct its non-emphatic form, I have to 'borrow' the thought from the first clause to make it meaningful, and I also have to construct the sentence in normal order (not inverted). This is the result:
"Coffee has caffeine too."
In the non-emphatic or normal form, a sentence uses only the main verb (in this case, "has"). In the emphatic form, on the other hand, the verb is in the following format: auxiliary verb + main verb (does + have).
If used together with the first clause it would read this way:
"Tea has caffeine, and coffee has caffeine too."
Notice the redundant use of has caffeine. I firmly believe that the reason why the writer of the sentence decided to go for inversion and use the emphatic form in constructing the second clause, as well use so in place of too, is to avoid redundancy.