No, you don't grout in a shower drain cover. It is important to ensure the area around the drain is well sealed and that there are no gaps or spaces between the tiles and the drain:
• Take time to ensure all tiles surrounding the shower drain are level with each other.
• Use a sealant or caulk specifically made for bathrooms to fill any gaps between the tile and grate of your shower drain cover.
• Test caulking's flexibility by pressing on it gently with your finger after it has dried. If it does not give way easily, then you have done a good job sealing up your drainage system!