In practice, most Americans have the verb agree with the noun closest to it. So "A large number of people are coming" would be most common. But yes, collective nouns are treated as singular in AmE; we would never say "The band are touring the country" or "The government are spying on us".
M.G. Doyle raises a good point, which has to do with formal and informal registers. In Standard Written (American) English, the grammatically correct form is "A large number of people is . . . " because 'number' is the subject, and it's singular. The subject of a sentence is never found in a prepositional phrase such as 'of people;' a prepositional phrase always acts as a modifier, never as the subject itself. So, the subject requires 'is' rather than 'are.'
In spoken American English, which of course tends to be less formal overall, many people would use 'are' because, as M.G. has pointed out, it's the noun that is closer to the main verb.