You're close, but still misunderstanding it.
With P2SH^2 when is the data hashed by the script first published? Remember that P2SH^2 is distinct from regular P2SH.
We'd have to wait for an actual P2SH^2 implementation.
But from the P2SH^2 discussion, it looks like the data would be relayed/published along with the P2SH^2 even though it will not be not stored.
Just like P2SH, we'd be pushing transactional data from one end to the other only to add even more bloat in the end. One of the reasons given to deter OP_RETURN was that blockchain bloat would further reduce the economic incentive for full nodes. It's a bit absurd since there's very little economic incentives for full nodes now. The fees only go to the miners.
As the blockchain grow and grow, the only incentives for full nodes may actually come from projects on top of Bitcoin such as the current MsC/XCP crowds.