The part that it makes tough is getting that interview. If it's a company that bothers to click your resume's Github link and see some work samples, you're probably OK. If it's a big company with a crappy HR filter on incoming applicants, you might have to find another way to get a foot in the door.
I know Google has a pretty good chunk of people without CS degrees. I'm curious if any self-taught people manage to get in there as a first job in the industry, like grads hired fresh out of college.
My concern is in situations like the above, the ONLY way such a recruiter can qualify you is based on value of your degree parameter. Which means if the company you are applying for goes the traditional big-bizz HR approach, go get a degree in CS from a Brand-name institution. Otherwise, focus your efforts on getting interviews with whomever your direct supervisor will be. That however, is easier said than done.