No, deleting tags, or any other terms, does not remove any posts. It shouldn’t even “touch” posts table. All it does is (you can see the code yourself: https://core.trac.wordpress.org/browser/tags/4.9.6/src/wp-includes/taxonomy.php#L1664):
- remove given term
- remove this term from all posts
- refresh caches
But… There are some hooks in it, so some plugin or theme can modify this behavior…