Connect a M.2 (B & M) key SSD into a B socket

It should... a B&M module should work with either a B or M socket, this is by design.

The B interface provides x2 PCIe, SATA, USB 2.0 and 3.0, audio, UIM, HSIC, SSIC, I2C, and SMBus support. The M interface provides x4 PCIe, SATA, and SMBus.

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If your module is B&M SATA (most likely), connecting it to a B or M socket should work fine since both types support SATA.

Of course, being a bootable device is another story, this depends on your hardware and UEFI.