Hey David,
Good question! I have not personally tested The Events Calendar with that exact setup. The plugin, however, is a free download and I would suggest giving it a try for yourself to make sure it integrates smoothly.
I can say for sure that the plugin is compatible with WordPress and that I have no seen any reports of issues with GoDaddy.
Sorry I don;t have a more detailed answer here, but does this at least help? Please let me know if you have any other questions and I’d be happy to help as best I can. 🙂
Cheers!
Geoff