By 'adverbial phrase' I'll assume you mean phrases that function as an 'adverbial' (as opposed to adverb phrases, which are defined as phrases headed by an adverb). The answer to both parts of your question is no . Prepositional phrases can function as adverbials, complements to verbs and adjectives, and also as noun modifiers: Adverbial: 'I cut it with a razor blade '.
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