louieakil it can be done, but you'll still need Composer to install extensions or Flarum updates.
If you run all Composer commands locally and upload files to the server each time it can be done.
However if you don't have SSH access at all, you won't have access to the php flarum info or php flarum cache:clear commands and this can seriously complicate troubleshooting an issue, should you encounter one later.
You should make sure to run Composer locally with identical PHP version and modules as the server, to be certain to send libraries that are compatible with your server.
So in summary it can be done, but we might not be able to help you effectively or at all if something goes wrong.