Gutenberg custom block using only register_block_type() and HTML

No, blocks are built with more than HTML – they need JS and PHP.

However, you could add an HTML block wherever you need it, then click the More Options dots in the block’s toolbar, click Add to Reusable Blocks, name your block, and save it. That block will then be available to use wherever you want it, and if you edit it, that will apply the changes everywhere.