No - for SATA drives.
Yes - for NVMe drives connected via PCIe bus.

SATA controllers operate sequentially whereas NVMe controller can execute parallel commands using multiple PCIe interface lanes.

“Multiple IO channels or communications pathways between the host and device that carry commands and return status may be created. These IO channels are implemented through command submission and command completion queue pairs. Having the ability to create multiple IO channels, which may operate in parallel and independent of one another, is fundamental to the transport model of NVMe.”

See NVM Express - Wikipedia