It depends on how the PCB was Designed.
Typically speaking., no... you'll be fine with a 6-Pin PCI-E Power Connector., just keep in mind you'll be limited to the Default Reference Power Limits of Polaris (10),. i.e. it'll behave like a Reference RX 480; instead of an RX 580; which does need an extra 15w for Reference that the PCI-E Slot and 6-Pin PCI-E Power doesn't quite provide.
I mean they technically can, but not within the PCI-E Specifications; and so few Boards are designed to go beyond said Limits.
Still there is a simple way to find out... connect the 6-Pin., if the Card and System Boots; then... yeah it'll be fine., if it doesn't, then no; you'll need the 8-Pin Connector. Chances are it'll be fine, as most AMD Card Designs don't physically limit Voltage Draw between 60-80% like NVIDIA Card Designs do; which eh, it is arguably better; but is also what leads to the High-Performance NVIDIA Cards having like 3x 8-Pin on them., which is just silly; as such can draw up to 450w on their own., plus 75w from the PCI-Slot.
A key difference between using a 6-Pin and 8-Pin is well... 150w Vs. 225w (Total) Draw.
Typically speaking the Reference RX 580 requires 165w., but as noted; if that's not available then either it will (or you can Manually set the Power Target to -10% … and it'll effectively run like a Reference RX 480.
