Yes, you are right. But this will only work if all your dependencies (composer stuff) and compilations (node/yarn) have been successfully loaded and compiled on your system.
composer install will add all the necessary php code for a Roots theme to your project.
On shared hosting environments the ability to run composer/node is typically not available, so you have to do
composer install and
yarn run build:production on your computer before you can upload it to your site (whether you choose to upload it through FTP or as a ZIP file is a personal preference).
If your WordPress installation is on a Digital Ocean droplet (or any other setup where you are the sysadmin), you can ssh into the server and install all your composer dependencies and compile your assets using the above commands. This will only be necessary if you did not/cannot run these commands on your local machine - for instance when you are developing on the live server.
I hope this helps a little, let me know if there’s anything else I can help with.