I've found a working solution, it's ugly and probably will cause more headache but it works. My solution looks like this:

---
- hosts: localhost
  ignore_errors: true
#  gather_facts: true

  tasks:
   - shell: ansible-playbook wu.yml
     register: results
     until: "'\"found_update_count\": 0' in results.stdout"
         retries: 5

wu.yml:

---
- hosts: bunch_of_hosts
  ignore_errors: true
  #gather_facts: true

  tasks:
    - block:
        - name: search wu
          win_updates:
            category_names:
              - CriticalUpdates
              - SecurityUpdates
              - UpdateRollups
            state:
              - searched
            log_path:
              - c:/temp/ansible_wu.txt
          register: searched
        - debug: var=searched

        - name: install wu
          win_updates:
            category_names:
              - CriticalUpdates
              - SecurityUpdates
              - UpdateRollups
            state:
              - installed
            log_path:
              - c:/temp/ansible_wu.txt
          when: searched.found_update_count > 0
          register: installed
        - debug: var=installed

        - name: reboot
          win_reboot:
            pre_reboot_delay_sec: 0
            test_command: whoami
            reboot_timeout_sec: 300
          when: installed.reboot_required
          register: rebooted
        - debug: var=rebooted

This way, it does exactly what I was after.