I'd love to be able to use mIRC to pull the text from a single cell in column D in this spreadsheet: https://docs.google.com/spreadsheets/d/1v8pzFlwB-mG8VJYG_WxoYh88C3c8XsrexMgSP0d1OiI

And save that text to a text file.

Is this something mIRC can do? And if so, how?

The short answer is yes, you can do it by using the API and sockets.

It can be a bit complicated and requires effort, but it's definitely doable. You just need to find someone who can be bothered to do it and knows how to do it.