Can a non-enumerated device conduct DMA operations?
Strictly speaking, "enumeration" is the process where the BIOS/OS asks all devices what their IDs are. If no driver is found for some device, it still has been enumerated, the OS just does not know what to do with it.

The PCI Express specification says that a device is allowed to issue memory or I/O requests only when the "Bus Master Enable" configuration bit has been set. This bit is usually set by the driver, but your device could simply ignore it (the pcileech device obviously does this).

Memory requests go to a specific address. In many systems, this address is the same as the memory address, but modern systems have an IOMMU that maps between PCIe bus addresses and memory bus addresses, in order to allow efficient hardware accesses in virtual machines. When the IOMMU is enabled, memory requests have an effect only when they go to a bus address that has been registered by the device driver.