I'm having trouble understanding the question. Rather than saying that "all adjectives in Chinese can function as verbs", I'm wondering whether the more normal formulation might not be "in Chinese, adjectives are classed as a type of verb". There are many ways in which adjectives like 高 and 好 are the same as verbs. Like verbs, they can occur in the forms 高了，高着呢，高不了, etc. They can occur predicatively and attributively (in which case they resemble relative clauses). However, they must be regarded as intransitive verbs as they normally don't take objects.
I don't think Chinese is the first language for which it has been claimed that adjectives belong with verbs.
I'd like to expand my answer by quoting here from Pulleybank's Outline of Classical Chinese Grammar:
1. Classes of Verbs
Adjectives, e.g., shān gāo 山高 'the mountain is high,' form the first major subdivision that needs to be distinguished among naturally predicating words in Chinese. Though, as words that form predicates without the addition of a particle, they belong with verbs rather than nouns, they differ from verbs proper in their syntactical behaviour in a number of ways. They are sometimes called 'stative verbs' but there are objections to this, since transitive verbs such as zhī 知 'know' also denote a state rather than an action. A possible alternative would be 'quality verb,' but as a class they correspond closely in meaning to adjectives in other languages and we shall continue to use this traditional term.
Adjectives must be classed as verbs in Classical, as well as Modern Chinese, since they form predicates without a copula or final yě 也, are negated by bù, and take the aspect markers yǐ 矣 and wèi 未. Nevertheless, as their behaviour with kě 可 shows, they differ from intransitive verbs in their syntax and have certain resemblances to nouns.
Here Pulleybank is referring to the fact that intransitive verbs and transitive verbs in an active sense use kěyǐ 可以 'possible', e.g., wáng kěyǐ shā rén 王可以殺人 'the king can kill a man', whereas adjectives, like nouns, require the copula verb wéi 為, e.g., kěyǐ wéi měi hū 可以為美乎 'can be (or remain) beautiful'.
Incidentally, Pulleybank is not talking about adjectives being used as verbs here. He is talking about adjectives as verbs.
While Classical Chinese is a rather different language from modern Chinese, and Pulleybank is not a theoretical linguist, I think the passage quoted above is a good illustration of the point. As to whether this applies to all adjectives, I think Claw has pointed out a couple of interesting examples.
As for the function of 很, it is not a copula, as others have pointed out. To call it an 'adverb' isn't necessarily very informative since 'adverb' as a part of speech is a bit of a grab bag. (Incidentally, Chinese grammarians apparently class 今天 'today' as a noun, even where it is clearly functioning as a 'sentence adverb'.)