The short answer is, most likely, YES.
If your tiles are in relatively good condition-evenly placed, without cracks, and not appearing to retain any moisture-then you can probably leave them underneath your new layer of flooring when going about installing a new floor or even a backsplash.
Assess the existing tile!
Before you begin flooring over tile, conduct a thorough assessment of the base layer to pinpoint any surface irregularities, which can cause foundational problems down the road. Mildew and deep discoloration in the grout often signal an absorption issue–meaning that trapped water has damaged the grout and could thus rot the new tile from below. An absorption issue will fester and worsen when the tiles are covered up. Likewise, if the original tiles were not properly installed, the new overlaying flooring won’t lie flat or line up. If you do discover either of these issues, it’s better to start from scratch than to install new flooring over the existing tile.