So remember what Maize said to Shallan and how she was stuck, trapped to Roshar? I think it's due to the type of investiture that she uses. I think having Rysn bond a Spren would lock her physically onto Roshar as well, meaning that the Dawnshar itself would be trapped in the same system as Odium.
Now if Odium where to gain the power of the Dawnshard... i'm betting we'll have to RAFO.