No. Each disk in the parity array is an independent filesystem, the user shares are a merged directory tree across same named root folders on all participating disks.
Technically the answer to your thread title is yes, you can create vdisk's larger than the available space because they are created sparse, and only occupy the space actually written inside the image. However, as you found out, when the containing disk runs out of space, the vdisk doesn't have anywhere to put the data, so the virtual filesystem doesn't work correctly.
Instead of using the parity array, you can assign multiple disks to a pool, which can use either BTRFS or ZFS RAID levels to create a single filesystem spanning multiple physical disks.