If I purchased a wordpress theme from a third party, can I upload it onto godaddy and use it as the theme for my Managed Wordpress site?
You should be able to add your theme without any problems using the instructions for adding a new theme found here: https://codex.wordpress.org.
and would GoDaddy still notify me and manage the updates for the theme?
the link doesn't work
Sorry about the link not working! Try using this article to help add themes https://docs.presscustomizr.com/article/141-how-to-manually-install-or-update-a-wordpress-theme. All the best!