Jp
No they won't work that way
I agree with this reply.
Water flows in a vertical direction through the unit - not sure which way though as I haven't opened it to have a look. As the resin settles down and some of it 'disappears', gravity will always ensure that the resin sits at the bottom. The only way for the water to pass through is through the resin.
If you put the vessel on its side, the resin will settle down onto the bottom of the vessel and there will be a gap/space along the top. Water passing through this space or channel will be out of the resin, so has less chance of being purified.
I haven't seen an Ionics vessel, so maybe the internals are designed differently, but mechanically, I can't see how they could get it to work, unless they specify which side the vessel is to be laid on.
Spruce.