Software update doesn't work. In response to this feedback, we’ll further improve Office 2016 for Mac’s support for VBA add-ins. Specifically, we’ll be adding Office ribbon customization via Ribbon XML, and making other improvements to Word, Excel, and PowerPoint for Mac to match their Windows desktop versions.

Doing further research, I came across Robert Knight's comment on this question and built an HTTPGet function using his execShell function to call curl. I've tested this on a Mac running Mac OS X 10.8.3 (Mountain Lion) with Excel for Mac 2011.

The answer above from John Stephens is fantastic (please upvote it!), but it no longer worked for me in the more recent Excel:mac 2016, with an error that the code needs to be updated for use on 64-bit systems.