Hi there, Gretchen–thanks for getting in touch. 🙂
Interesting question! I think the answer really depends on how the desktop and mobile versions of your site are currently tied together. If they are two separate installations of WordPress, then you certainly be able to install The Events Calendar on both sites, but would need to enter the content separately from one another.
We have seen one instance where a customer had a WordPress multisite installation and found a way to make the event widgets share content between sites on the same multisite network. That was a very creative solution, but did require a lot of custom development to pull off.
So, the short answer is that sounds like you might require entering content twice. Then again, that all depends on how WordPress is setup for you and to what extent you can customize the plugins.
Does this help answer your question? Please let me know if you have any follow-up questions here and I’d be happy to help. 🙂
Cheers!
Geoff