Would an American native speaker be able to hear a difference between /ʌ/ and /ɑ/ in pronunciation of "done" and "don" and recognize which one was said without a context? For me as a non-native speaker, they sound quite similar.
It's unclear what variety of English you're talking about. In General American English, they use /ɑ/ in words like bot, don, hot, cot and /ʌ/ in strut, cut, done. So /dʌn/ will be understood by natives of both the UK and the US as done.
However, /dɑ(ː)n/ will be understood by most Americans as don, but by British as darn because British English uses /ɒ/ (a rounded version of /ɑ/) in most words where GenAmE uses /ɑ(ː)/.