No, Vampires don't react badly to drinks, not even those with the withered stomach weakness, they can eat normal food and drinks just fine but their fun and hunger go down while doing so. If they have aforementioned weakness then they can't eat Sim food, not even Plasma fruit salad, without vomiting.
Caleb doesn't get any of the positive foodie moodlets drinking plasma, just the normal vampire ones and I haven't seen him get foodie moodlets from Sim food either, which is why I don't like that trait on him. But maybe the food he ate just wasn't high quality enough, who knows, I didn't test it throughly enough, to be honest. He can still enjoy the cooking show and enthusing about food, so it's not a bad trait for him, just rather pointless.
Personally, I would only let Caleb drink the high quality bar drinks to avoid that bad drink moodlet from his foodie trait but that's just me.
Yes, Vampires can get sick.