I’m not certain, but since blocks are not represented in the API, it seems unlikely.
I do know that you cannot copy page designer objects from one block and paste them into another page designer block regardless if it’s in the same or a different base.
Bummer. Airtable needs a “block export” and import. Or, a way to design blocks at the workspace level and simply share into bases where they are needed. Ergo - write once; run everywhere.
Apologies for reviving such an old thread, but if there's another response to this, I haven't found it. I'm curious if this functionality has been added as of the date of this post. If not, it is still a missing feature IMO.