A one week injury typically can last anything from 1 day to 13 days. Thus you can not be sure if he will be ready for you in the playoffs.
When was the player injured?? he might still be able to be available for playoffs depending on when he was injured and a bit of luck on how long that "1 week" is going to be.
And yes you will have to train GS to maintain his GS as no minutes will result in a drop in GS.