I assume you are after something gold or silver-type. I've no experience of overlockers, but you can get some metallic type multistranded threads that will go through a sewing machine. I think they are meant for machine embroidery, and are quite fine and probably not as hardwearing as ordinary polyester thread. Only suitable for decorative bits rather than anything that will take any stresses, IMO. If you're edge-finishing they'd probably be quite delicate looking.
I know there are thicker lurex threads available for crochet, but doubt they'd go through a machine.