Yes I would think that it would use something else (probably overlayfs), although there are other issues to contend with (for example you cannot use overlay on ZFS see Docker with overlay driver in LXD cluster not working)
Depending on whether you don’t need efficient snapshots, then using a dir pool on ext4 might be a less problematic approach. Alternatively you could also try using an lvm pool using ext4 as that would then support ‘proper’ snapshots of the container itself.