When shopping for marble tile for a backsplash my husband decided he liked "groutless tile", something I hadn't seen before. These are small mosaic size pieces mounted on 1 foot sq. mesh, with so spaces in between. We bought 2 kinds, 3/4" x 3/4" (20 x 20 mm), and a brick shape, ~ 5/8" x 1 1/2". The bottom row of the backsplash would be large 12 x 12 marble tiles: the smaller mosaic pieces would be above the large tiles.

I am skeptical about the very idea of a groutless tile, but this was the only thing he liked, so I'd like to make it work. I'm thinking, compromise by grouting the large tiles, and horizontally grouting between the brick mosaic and the square mosaic. (Then seeing if I can't force some grout in between the mosaic anyway) As long as it's colored to match hopefully it will still have that sleek look he liked so much. Then use many coats of sealer...
This backsplash is NOT behind the stove: there we have a large piece of granite. So no cooking splashes to worry about.

Advice, please! Thanks!

Heres a photo of a tumbled marble tile I did which is groutless.

Hard to see in the photo but every pc is tight together. The bottom is caulked to the granite counter top.

These pcs were bigger than your planing to do but I see no reason not to do groutless as long as they fit tight together.
Just have to be carefull when setting with thinset as any thinset on the edges will cause problems.

Amazing. Looks grouted to me!