Possible: Technically yes.
Let me state it this way: I got some hardware and I can do with it whatever I want. I them give or sell it to you with it configured to perfectly act like an external hard drive.
Would you be surprised if it had an undocumented command which would give me access to the data?
I am guessing we both agree that the answer is: No. Ofcourse we could not be surprised.
That leaves generic drivers. I also see not problem there. The generic driver will support all the normal commands, and we could for a combination of them and trigger on that. E.g. if someone reads sector 3, 14, 15, 92, 65 and 35 and thus this 42 times with a delay of at least 5 seconds between sector reads. (or make up your own unlikely access pattern, maybe using a special value when setting a system protected area or anything else a normal user would be unlikely to do).
That means we have extra capabilities ont he drive and a way to trigger them, causing the drive to do whatever we want. Which could include returning the entryption password of the drive, or the raw data written to a sector.
Thuis the answet to the question:
Is this possible? is a big yes.
Which is not the same as is this likely. But technically: sure, it is possible.