Basic (desktop) functionality may work (or may not). It's never recommended to run a GPU without all aux power plugged in, though. If your PSU only has one 8-pin GPU plug it may not be powerful enough for an RX 570. Please list your exact PSU model.
It's possible to get an adapter to turn a pair of 4-pin molex connectors into a 6-pin but you've got to be careful. Many, many adapters like this are not up to spec and can be a hazard or even damage your new (used) card.