Will mysql still get apt-updates then if installed like this?

Sure

An other way simple

- name: Add public key mysql from ubuntu server
  apt_key:
    keyserver: keyserver.ubuntu.com
    id: 467B942D3A79BD29
- name: add mysql 5.7 apt repository
  apt_repository:
    repo: 'deb http://repo.mysql.com/apt/ubuntu bionic mysql-5.7'
    state: present
    update_cache: yes
- name: Install mysql client 5.7
  apt:
    name: mysql-client=5.7*
    state: present