Yes, on a file sharing website I use, there is usually a captcha which then reveals the download link. On my iPad Mini 2 the download link was there but no captcha (no box or image or anything). When I click the link, a message says "Wrong captcha", so I know it's there, but not displayed. I finally discovered that some browsers can let you switch user agent (i.e., spoof another browser). I stumbled across an app - Documents 5 - which apparently is a multifunctional app, one of them being a browser. When I set the user agent to IE 9, the captcha shows up. However I had some issues with the download that I cannot attribute to the browser or iPad.
Another browser that switches user agent is Mercury, but it didn't help me.
Another suggestion I've read is to turn off ad blocking in the browser, which made sense to me because these captchas are basically Ford ads, but on the site I use it didn't help.