I used 511 impregnator sealer as per the instructions- my backsplash is a medium grey marble herringbone, and the grout was a darker grey color (avoiding white for grease/cleaning issues, I've got enough to worry about with a marble and white kitchen haha, without having to scrub all those grout lines with a toothbrush!) and before the grout went on i put the sealer on the tile - something about a "grout release" to avoid any possible grout staining the lighter tile, and now i'm re-sealing everything again with the grout on.

I don't have a tile backsplash (I may be a permanent member of the ABB club!!!) but my parents did seal the grout on their tile splash.

I don't know if it's particularly necessary for grout- i used mine more to protect the stone. I'm not an expert, but based on some other pro opinions on here, there is much debate about what exactly needs to be sealed vs what doesn't.

Floors get "traffic" backsplashes don't....

for me, it was more of a helper to keep the stone tile easier to clean/not stain with grease.

Yes, you seal grout on the bs. I have two words for you, tomato sauce. Or how about cherry juice? And yes even grease stains. It takes a minute to seal it. No reason not to.

I sealed my travertine before it was installed and then after installation did grout and stone again. Almost three years old and still looks like brand new. It is really worth doing.