No, they pick them up and carry them around. The big issue is that they are bulldozers, and if your frags or rocks are not secure, this can be a big problem.
Slate pencil urchins are likely to be predatory but others are not as much of a risk.
I generally do not suggest people keep the longspine urchin Diadema which gets very large and can cause serious wounds. The best urchin overall, IMO, is the blue tuxedo urchin.
Also note that water parameters and acclimation are very important.