....I suspect your opponents would be slightly less likely to do so than if you were to play Omen Machine in a vacuum. Multiple instances of card draw prevention are redundant, multiple Omen Machine triggers are not.
....unless you're using it as a way to nullify removal and make it more difficult to get off the battlefield, in which case the answer is 'maybe'. I played a game once where a Ramos, Dragon Engine chaos deck played out Omen Machine.... while the other two players in the pod were myself playing Tasigur, the Golden Fang (who doesn't technically draw cards with his ability) and another player running The Locust God. As you may imagine, I fought pretty hard to keep Omen Machine on the battlefield.