Can a black widow spider eat a tarantula?

Yes, a tarantula Hawk could certainly kill a black widow spider if it wanted to. A black widow spider would be too small for a tarantula hawk to bother with most of the time.

Actually, black widows are a favorite meal for some types of mud wasps. The wasp will sting the spider - paralyzing it - not killing it. Then take the black widow and stuff it inside the nest it's making for it's off spring. When the wasp larvae are growing, they'll feed on the paralyzed spider. This is the same basic thing that a tarantual hawk does with the much larger tarantula spider.

While you can find video's of black widows appearing to catch and kill wasps, this is definitely the exception rather than the rule. A wasp can run into trouble if it finds itself tangled in the spider's web, though most of the time they're able to navigate their way around it and deliver the paralizing sting before carrying the spider off to it's nest.