Well, yes. That's exactly what they do. It is important to point out, however, the difference between "allegations" and "alligations"; because, to the best of my knowledge, while allegators are excellent at allegating, they are actually fairly unskilled when it comes to making allegations.
I agree with Lisa HW and I too believe that alligators alligate better than anyone. In my wide experience, I've never met an alligator that couldn't alligate - it's what they're mostly known for except for the occasional one who's known to tailgate.