Yes, it should work. You just need to follow simple steps:
1) Take Files/Folder backup and Database Backup
2) Set them up in your local installation
3) Make changes of website URL in
core_config_data table in database. Replace current LIVE URL to your local URL
4) Update database connection credential in
5) Clear your caches and check if there aren't any custom redirection rule in .htaccess file. Adjust them if required.
It should make your local copy run. If you are facing problem, you should deploy your content once and also recompile your setup.
Hope it helps.