結論

結論から言うと、vagrant box addは実行しなくても良い。
vagrant up の中で boxファイルがローカルになければ、boxファイルをダウンロードします。
Getting Started-Vagrant by HashiCorp
vagrant box add は、個別で作成したboxファイルをローカルに登録する場合は必須と思われる。

やってみた

実際に、vagrant initとvagrant up を実行して、boxファイルがダウンロードされました。

vagrant init を実行。

$ vagrant init ubuntu/trusty64
A `Vagrantfile` has been placed in this directory. You are now
ready to `vagrant up` your first virtual environment! Please read
the comments in the Vagrantfile as well as documentation on
`vagrantup.com` for more information on using Vagrant.

vagrant up を実行。


$ vagrant up
Bringing machine 'default' up with 'virtualbox' provider...
==> default: Box 'ubuntu/trusty64' could not be found. Attempting to find and install...
    default: Box Provider: virtualbox
    default: Box Version: >= 0
==> default: Loading metadata for box 'ubuntu/trusty64'
    default: URL: https://vagrantcloud.com/ubuntu/trusty64
==> default: Adding box 'ubuntu/trusty64' (v20180919.0.0) for provider: virtualbox
    default: Downloading: https://vagrantcloud.com/ubuntu/boxes/trusty64/versions/20180919.0.0/providers/virtualbox.box
    default: Download redirected to host: cloud-images.ubuntu.com
==> default: Successfully added box 'ubuntu/trusty64' (v20180919.0.0) for 'virtualbox'!
==> default: Importing base box 'ubuntu/trusty64'...
==> default: Matching MAC address for NAT networking...
==> default: Checking if box 'ubuntu/trusty64' is up to date...
==> default: Setting the name of the VM: ubuntu2_default_1537621833292_4472
==> default: Clearing any previously set forwarded ports...
==> default: Clearing any previously set network interfaces...
==> default: Preparing network interfaces based on configuration...
    default: Adapter 1: nat
==> default: Forwarding ports...
    default: 22 (guest) => 2222 (host) (adapter 1)
==> default: Booting VM...
==> default: Waiting for machine to boot. This may take a few minutes...
    default: SSH address: 127.0.0.1:2222
    default: SSH username: vagrant
    default: SSH auth method: private key
    default: 
    default: Vagrant insecure key detected. Vagrant will automatically replace
    default: this with a newly generated keypair for better security.
    default: 
    default: Inserting generated public key within guest...
    default: Removing insecure key from the guest if it's present...
    default: Key inserted! Disconnecting and reconnecting using new SSH key...
==> default: Machine booted and ready!
==> default: Checking for guest additions in VM...
    default: The guest additions on this VM do not match the installed version of
    default: VirtualBox! In most cases this is fine, but in rare cases it can
    default: prevent things such as shared folders from working properly. If you see
    default: shared folder errors, please make sure the guest additions within the
    default: virtual machine match the version of VirtualBox you have installed on
    default: your host and reload your VM.
    default: 
    default: Guest Additions Version: 4.3.36
    default: VirtualBox Version: 5.2
==> default: Mounting shared folders...
    default: /vagrant => /Users/xxxx/Vagrant/ubuntu2

ゲストOSにログイン


$ vagrant ssh
Welcome to Ubuntu 14.04.5 LTS (GNU/Linux 3.13.0-158-generic x86_64)

 * Documentation:  https://help.ubuntu.com/

 System information disabled due to load higher than 1.0

  Get cloud support with Ubuntu Advantage Cloud Guest:
    http://www.ubuntu.com/business/services/cloud

0 packages can be updated.
0 updates are security updates.

New release '16.04.5 LTS' available.
Run 'do-release-upgrade' to upgrade to it.


vagrant@vagrant-ubuntu-trusty-64:~$

vagrant box listでも確認


$ vagrant box list
ubuntu/trusty64     (virtualbox, 20180919.0.0)

まとめ

Project Setupは、vagrant box add も含めて説明しているページのようだ。
個別で用意したboxファイルは、vagrant box addで追加する必要あり。
boxファイルをダウンロードしてくるのであれば、init と upだけでOK。
Project Setup - Getting Started - Vagrant by HashiCorp