Hello, from everything I have read, and my own experience it's not likely... yellow tangs are classified as "herbivore" so stick to eating mostly marine plants, and the occasional substitution of mysis along with whatever else we feed them...skunk shrimps have a lifespan of around 2 years in the wild, and sometimes as long as 4 years in captivity... I guess it could be possible it was being overly aggressive and killed it but, that seems unlike... I've had a mated pair going on two yrs now and none of my tangs have ever been caught in an aggressive altercation with either one.
Did you find the shrimp dead and being picked over as a food source by the Tang?