Certificates by edX are, as a general rule, held in great esteem and value by employers. This is because it is the most popular e-learning platform, with partnered universities and prestigious institutions that give credibility to the skill sets developed and taught by the courses on this platform.
Upon completion of an edX course, you get the option to pay for a verified certificate of the course, and this is what is recommended if you want possible employers to care about the course in any way. This verified certificate can add a lot of value to the skills and qualifications you are claiming to have for the possible job in question, and they are verified by prestigious institutions that make it official and recognized.
So essentially, the answer is yes. Employers do care about edX certificates, and purchasing a verified certificate at the end of your edX course is well worth it so that you have the official accreditation and recognition.