It is technically possible. When you test for covid19 you give your cell number as part of the routine information collection and if your test results are negative you should receive an sms from NHLS informing you about the results. Take that cell number and load it on a tracking app and rhe thing is done. I'm not saying this FB post is legit and it is happening in SA. But It is the case in South Korea though. They see making use of such an app in order to trace contacts of positive patients AFAIK.
@Grand Guru The FB post is legit - as soon as I read it I checked my phone and I was startled to see the Covid app on it!! I wouldn't have even realised it was there if someone had not told me.