Short version: Yes you can.
Long version: Yes you can transfer the storage over. However it's not guaranteed to work completely due to missing drivers. I expect Valve to integrate the needed drivers to the current SteamOS upon the release of the new version. It doesn't make sense to have two different SteamOSes. So I expect the need to update the the latest SteamOS then transfer it over and it will work just fine, as it should.
Update: Today they pushed the oled changes to the common repository. So after updating to the latest SteamOS you will be able to move your SSD to the OLED Deck.
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