I know I would. If someone gives you a choice A or B that both screw you over, there's always an option Z somewhere. It might be so outrageous they don't expect it but it's there.
However usually it isn't necessary. I've been put in situations where I had to do something unethical. I've refused. And every time that choice was respected. Only if I'd have been punished for it would I have considered more severe options.
But really if you take a hard stand and have good reasons, reality tends to bend a bit further than I expected.
And yes I know what these jobs are like. I have worked in that industry a long time. With both very good and very terrible employers.
We could discuss in a sociological basis on how Capitalism today uses this workforce for degrading jobs, though requires a large dialogue that HN is not the place.
https://www.reddit.com/r/callcentres/comments/1iiqbxh/the_re...
Abuses done by customers: https://www.bbc.com/news/business-59577351