Not really, but it depends on context. The nuance is often difficult to detect when written. When spoken, a phrase like "quite extraordinary" or "quite brillian

Not really, but it depends on context. The nuance is often difficult to detect when written. When spoken, a phrase like "quite extraordinary" or "quite brilliant" would usually be a superlative, as you suggest, but it would usually be indicated by emphasis on the "quite". And the adjective itself already has to be quite strong, so "quite good" will never really mean "great".