Will agitated already set custard re-set again?
No, it will not set again at all. 

The explanation behind it: The custard is not a gel, it is a mixture of proteins, fat globules and other stuff swimming in a liquid (or maybe gel?). You start off with normally folded proteins, which during heating lose their quarternary structure and "hook" each other, thus creating a kind of mesh, filled with the fat emulsion. Once you break that mesh apart by agitation, it will not reform at all, since you cannot refold the proteins.