It was (and may still be) possible to make an older version of Pocket Edition run on Linux through unofficial shenanigans, but the official launcher says "Not playable on this device".
minecraft.net also explicitly says: "Minecraft: Java Edition runs on Windows, Mac, and Linux; Minecraft: Bedrock Edition runs on Windows. Deluxe Collection content only runs on Minecraft: Bedrock Edition on Windows."
Other unofficial shenanigans that may or may not work include but are not limited to: Running under a VM, running under something like Wine.
So, yes, technically it runs, but Microsoft are pretty clear that it's not supposed to.