Does doing online courses on sites such as Coursera and edX actually benefit your career?

Do employers even recognise them?

I don't want to spend my money if they aren't going to improve my employability

I think that depends on the kind of certificate, the topic and the employer. The data science Micromasters and Master Track qualifications are solid foundations, and they are exactly what they seem: proof you can master the content of well-designed master's degrees.  The verified attendance certificates show that you can click next on a web page, understand the course language, and have real ID. So, it depends on your employer. I would certainly take someone seriously who had a Micromasters from a solid course. 

Yes and no. They can be a great, cost-effective way to skill-up in various business topics. That alone might be worth it for some.

I guess they can look good on a CV as well? Some courses are associated with strong school brand names, which can draw attention when applying to jobs (or jockeying for a raise / promotion in your current company). But in most cases just having a certificate will not lead directly to a new job. 

As you might be aware by browsing around these forums, the real value of a strong MBA would be the networking opportunities and job connections, which are provided by business schools, none of which would be really available as part of Coursera / edX certificates.