Can adverbs be qualified as transitive/intransitive?

In traditional grammar, words such as before were given different parts of speech according to what words they appeared before. According to this treatment we would see the following classifications in the following examples:

• I saw her before [the concert started]. (conjunction before clause)
• I saw her before [the concert]. (preposition before noun phrase)
• I had seen her before[]. (adverb without following complement)

Since the beginning of the twentieth century, some linguists have been arguing that this type of classification is silly. After all, we don't do this with verbs:

• I know [the doctor will be there] (verb before clause)
• I know [the doctor] (verb before noun phrase)
• I know []. (verb without a following complement)

In modern grammars such as The Cambridge Grammar of the English Language words such as before and after are prepositions in each of the examples further above. This is sensible because these words retain the same syntactic properties regardless of what kind of complement they take.

In the example I have seen her before the phrase before can be analysed as an intransitive use of a preposition. In the OP's example the word afterwards can be analysed as a preposition which is always intransitive. However, grammarians would not normally refer to afterwards as an intransitive adverb. The reason is that if its an adverb, then it's intransitive anyway. Adverbs hardly ever take complements - they're nearly all 'intransitive'.