Yes you can, I am responsible for taxing my Leaf and used my road tax exemption on my saab.
Phone Motability to discuss it. They sent me a copy of the V5 and when the tax reminder came in to them they forwarded that to me. You still have to go online (or to a post office?) and do the paperwork to tax the EV but obviously the cost is £0.00 ? Keep an eye on them though cause one year they just done it themselves so it might cause an issue.
I then taxed my saab convertible which saved £565.00 this year, if it hadn’t been for this i wouldn’t have kept it for so long (7 years) and only sold it last month ?