Yes. You will have to.
Currently the websites are under /home. If you mount a new partition to the same folder, the current contents of /home will disappear (not deleted). And you will have no access to it. So best to move the files to a backup folder. Then move it back after you mount it.
I prefer to mount the new storage to a tempory location, such as /mnt, and use rsync to archive the current contents of the new mount point, /home, for example. The new volume can then be unmounted. After it has been successfully copied, I like to delete the contents of the new mount point to recover the space. The new volume can then be mounted. Be sure to update the fstab so that the new volume is mounted automatically at boot.
My approach is service affecting and will require completion during a maintenance window. I prefer to conduct such operations from a temporary live boot environment like GRML.