I  think  there  is  a  method  to  do  that  yeah.  But  I  dont  think  you'll  get  any  points  for  her  if  she's  already  in  your  inbox  when  the  champ  chase  begins!

From what I can remember the method is force quitting the game when the champion claim screen pops up , when you login again the dot will be there and you'll be able to continue playing without claiming Scyle. ( Not sure if it's the exact method as I haven't done it in months ) 

you dont get any points if you get her from you inbox, (the points get awarded when she hits the Inbox not when you claim her form the Inbox)

so unfortunately the answer is no, you cant save those points for a champion chase later on