Not exactly, during the latest event arika had before this one in progress, the king told arika will have 2 lifes and 2 husbands, and kurt will be the fake one of course since arika will pretend she still loves kurt and that his baby is the one in her belly.
However, the king told her that at some point he will get bored and then will reveal the secret to everyone, arika agreed of course, and she even made some suggestions of what she will do when that happens.
So basically kurt will end up knowing the secret eventually, but its unsure for now if takeda will draw that scene or if the scene will be left to the imagination in the ending.