Does it makes sense to index a primary key if it is not used?
In MySQL, if you have an auto_increment column, it MUST also be a key/index (either primary or a unique or a non-unique one, so any index really) where auto increment column is the first in the index/key definition.

For any InnoDB tables that do not have a PRIMARY or UNIQUE NOT NULL key defined, MySQL will implicitly create (a 6-byte) internal key under the hood and use it as the clustered index.

This clustered key (the PRIMARY or the first UNIQUE NOT NULL or the 6-byte internal) is always included in ALL secondary indexes for InnoDB tables in MySQL.

In your situation, dropping the PRIMARY key will only result in MySQL creating an implicit one anyway (unless you define another PRIMARY or UNIQUE NOT NULL key explicitly). This also applies only to InnoDB tables.