Yes, this is possible, but you need to follow the instructions in the chapter on Replacing a failed RAID device in a logical volume:
Back up your data.
If your system supports hot swapping disks, swap one small disk for a large one; if it doesn’t, powerPower down the system, remove one disk, add a new larger disk, power the system back up; if the system doesn’t come back up correctly, you can revert the replacement (and ignore the rest of these instructions…).
Create a PV on the new disk (
pvcreate) and add it to the volume group (vgextend).Repair the logical volumes and the volume group:
lvconvert --repair vg_storage/lv_data lvconvert --repair vg_storage/lv_database vgreduce --removemissing vg_storageRepeat with the remaining disks until the entire array has been migrated.
The documentation you looked at assumes the old and new disks are connected simultaneously.