Quick answer: yes, but it doesn't make much sense.
In case you haven't noticed, the EVs you can buy today don't have, or even offer, manual transmissions. Not the Chevrolet Bolt, Nissan Leaf or any Tesla. And they likely never will, even though it's technically possible, as Engineering Explained points out. Actually, it's really not at all difficult to hook up an electric motor to a manual gearbox; it works in very much the same it does with conventional internal combustion engines. However, a manual, aside from the driving enjoyment factor, serves no purpose in an EV. None whatsoever.
Just because something can be done doesn't mean it should be – and that's the general philosophy of many automakers. More specifically, EV automakers aren't interested in manuals because there are quicker and more efficient transmissions out there.
Another issue worth pointing out is the fact that many EVs have their motors located at the wheels instead of the typical engine bay. Why direct power through a transmission only to have it returned to where it started from? Makes no sense. But we'll let Jason Fenske go into more of the intricate technical details. He can explain things much better than we can, hence the name of his YouTube channel.