The words here are grouped strangely. I think you should include "session" in the parentheses since the word "afternoon" is only here to describe "session." With that grouping, this is a gerund phrase, not an adverbial. An adverbial behaves like an adverb, while a gerund behaves like a noun. You can tell that it behaves like a noun in this sentence because it is the subject of the predicate "turned out." What turned out to have a big effect? (Going along to a single afternoon session) turned out to have a big effect.