It depends on the species of the wood, how close the kerf slots are, and how thin the web that is left is. But essentially they are pretty flexible.
While they do glue the sides to the top and back, what they are used for is to increase the glueing area to those areas. You still need to glue the sides to the top and back. Where the width of the kerfed linings comes in to it's own is when much or all of the glue join between top and sides has been removed to install bindings and purflings on instruments that have that extra trim. If the extra width of those linings wasn't there then the instrument would simply fall apart after those rebates were machined.