Luxury vinyl plank over ceramic tile?

[Adam Juodis]

Wondering if I can place luxury vinyl plank flooring right over existing ceramic tile without having to level the grout lines. The grout lines themselves are not much deeper than the top of the ceramic tile(See picture below). I'd rather not demo the existing ceramic tile, since my budget is pretty tight, and that will take a decent amount of time(For about 800 SF).

If I do need to fill the grout lines, what is the easiest and most cost effective solution? I've been reading some other media about this, but with the grout lines being small and not that deeper then the top of the tile, I can't image the vinyl planks 'dipping in' due to the slight imperfections of leveling. 

This is the type of flooring I am looking to put in, since it looks nice, its waterproof, and solid choice for wear-and-tear. Thoughts?