It depends… In theory the impedance presented to the radio on 30m is calculable by taking the capacitively reactive impedance at the base of the 20m quarter wave, then transforming it by whatever electrical length the feedline is on 30m, to arrive at an impedance expressed as Zin = R + jX, where X may be negative as it was at the base, or may have been transformed to a positive (inductive) impedance, at the rig end of the feedline. The special case is where the feedline is a (multiple of a) half wave on 30m, allowing for velocity factor, where the same impedance that was present at the antenna base is presented to the rig. Some ATUs might be able to cope with the reactive load. An L match would be able to transform the impedance to 50 ohms, however the conventional view of such situations is that the SWR will be high on that cable, increasing losses. it would be better to put the L match at the base of the antenna. Depending on how tolerant you are of losses, it might be usable but certainly not ideal. As Ron says, it it was great, everyone would be doing it. And there would be a bright shiny one offered on ebay.
My approach to a 20/30m vertical is to insert a suitable link in the 30m length to allow it to be the correct length on both bands. You have to drop the antenna to change bands, but that’s not arduous. The radials can be set up in advance to have two for each band so would not need to be link-switched but the antenna may well work better with 3 correct length radials for each band. I found quite good performance on 30m using the 3x 5m radials that were used on 20m without change. I haven’t compared that setup with 3 correctly sized radials on 30m.
73 Andrew VK1DA/VK2UH