The Song of Songs Typological?

Does the Song of Songs include typology?

Here is Graham Cole's definition of typology taken from his book He Who Gives Life (p. 289):

The idea that persons (e.g., Moses), events (e.g., the exodus), and institutions (e.g., the temple) can—in the plan of God—prefigure a later stage in that plan and provide the conceptuality necessary for understanding the divine intent (e.g., the coming of Christ to be the new Moses, to effect the new exodus, and to be the new temple).

This definition seems to summarize fairly well most if not all that this biblical phenomenon intends.  (And, incidentally, the prefiguring or pointing is by way of patterns and models intended and warranted by Scripture itself.)

Now, assuming Cole's is a good definition, back to the question: Does the Song of Songs qualify as typology or contain typological elements?  A second question: May we discern typological authorial intention?  One more: If so, how?