Yes, that’s possible. Pronouncing a curse before one’s own turn can make sense if the previous player has given so many hints during his riddle phases that all players know (or think they know) the solution.

Since you can’t propose solutions during the first riddle phase – although the other players are allowed to use curses – pronouncing a curse before beginning your turn is your only chance to be the first player to present the hopefully correct solution.

By the way: Pronouncing a curse means that you are interrupting the game, not that you're cursing someone.