OK, so as far as I'm aware Sega developed and produced the games but they originally brought the rights from Jay Geertsen. The last game in the main series was Columns III: Revenge of Columns and since then there's been various spinoffs but Sega's signiture puzzle series has been the Puyo Puyo series ever since Sega brought the rights of the game from Compile and assigned Sonic Team to the Puyo Puyo series. As far as I'm aware Sonic Team has not been involved in Columns.
But, as I said, Sonic Team have been making Puyo Puyo games since Puyo Pop for the Game Boy Advance (Minna de Puyo Puyo), the games since then, they have experiance in making these puzzle games that share a lot of similarities to Columns, if Sonic Team wanted too all it would take would be to modify the Puyo engine and script a new story around it.
If they did I hope they continue the phoenicial law established in the original games and not the Columns Crown game.