No. The Paldea Pokedex is different from the DLC Pokedex.
Since the DLC adds new Pokémon that isn't in the main game of Pokémon Scarlet and Violet, you can't transfer the new Pokémon that's confirmed to be in the DLC because those Pokémon aren't added to the game yet. The Paldea Dex doesn't have the new Pokémon in the DLC and therefore will not be able to be transferred / traded to SV. You just need to wait for the DLC to come out, and then you can trade / transfer the Pokémon you get in the GTS (that is in the DLC dex) into the Scarlet and Violet games.
