Hello there! This phrase is an adverbial phrase. The following link explains quite well why came along is an example of an Adverbial Phrase of Place:

http://www.grammar-monster.com/glossary/adverbial_phrases.htm

Where (Adverbial Phrase of Place)
An adverbial phrase of place states where something happens. For example:

I used to work in a fire-hydrant factory. You couldn't park anywhere near the place. (Steven Wright)
Opera is when a guy gets stabbed in the back and, instead of bleeding, he sings. (Ed Gardner)

Although came along does not describe a specific place, it is definitely an adverbial phrase.

Adjective phrases, on the other hand, are phrases whose head word is an adjective.

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