Minecraft Nintendo Switch Edition -nsp- -actual... Here
Yes, but with severe restrictions.
If you purchased the digital version of "Minecraft: Nintendo Switch Edition" before June 21, 2018, you can re-download it from the eShop forever. Go to your "Redownload" list in the eShop. It will appear as a separate icon from Bedrock.
However, if you are a new user, you cannot buy it. Nintendo and Mojang have removed the purchase option entirely. The only legitimate physical copies are the early print runs of the "Minecraft: Nintendo Switch Edition" box art (the one with the blue banner, not the red "Minecraft" banner). Minecraft Nintendo Switch Edition -NSP- -actual...
If you insert a physical Legacy cartridge into a Switch on current firmware (16.0+), the console will still run the Legacy version, though it will prompt you to update to Bedrock (you can decline).
Let's assume you have a legitimate dump of your own cartridge, or you are an archivist. You will run into signature checks. Yes, but with severe restrictions
A note on updates: The final Legacy update (v1.0.13) is essential. It fixes the "infinite loading screen" bug. Do not install v1.0.0 (the base cartridge version), as it crashes frequently.
To understand the current state of Minecraft on Switch, you have to look at its history. There are technically two versions of the game, though only one is readily available now. Let's assume you have a legitimate dump of
The Old Version: "Minecraft: Nintendo Switch Edition" Released in 2017, this was a standalone port based on the "Console Edition" codebase (similar to the Xbox 360/PS3 versions).
The Current Version: "Minecraft" (Bedrock Edition) This is the version currently available on the eShop. It uses the "Bedrock" engine, which allows cross-play with PC, Xbox, and PlayStation.
Before the "Bedrock" engine unified every platform under one codebase, Minecraft was split into distinct versions. The Legacy Console Edition (LCE) was developed by 4J Studios, not Mojang. This version ran on the "Console C++" engine.
For the Switch, this Legacy edition launched alongside the console in March 2017 (physical) and digitally in May 2017.