I think it won’t and you’ll have to extend the filesystem after the LV has been extended.
However I don’t really know how to do that.
You can locate a btrfs filesystem
$ sudo btrfs fi show
[sudo] password for [user]:
Label: 'default' uuid: d9320138-3142-4e44-93bd-a0e9ccbfef4a
Total devices 1 FS bytes used 18.99GiB
devid 1 size 20.64GiB used 20.64GiB path /dev/mapper/vg0-lxdPool
but as there is no mountpoint you can not maniupilate it with common
btrfs fi ... /path/to/fi commands cause it throws a
not a btrfs filesystem: /dev/mapper/vg0-lxdPool error at you. I guess this is due to the fact lxd seems to disguise the mount point of dedicated partitions used for pools somehow to the hosts OS. Is there anyway out of this?