Yes. Regardless of the plan you choose for your droplet, you get a VPS with full root access so you can install whatever you want on it. Check out this tutorial for instructions on how to install Apache, PHP, and MySQL on an Ubuntu 14.04 droplet:

• How To Install Linux, Apache, MySQL, PHP (LAMP) stack on Ubuntu 14.04

Once you’re done, you can use a SFTP client to upload your website to /var/www/html.