There would potentially be an age bias, though probably less in FB than a lot of other services you could cherrypick from. It'd also arguably bias older, since FB has been aging up in audience from what I can tell.
Without reading the study, though, possible they actually controlled that in the demographic profile for the ad.
Edit:
Going to the other thread confirmed this. From the paper,
"This study had several limitations. First, our sampling strategy selected for members of Santa Clara County with access to Facebook and a car to attend drive-through testing sites. This resulted in an over-representation of white women between the ages of 19 and 64, and an under-representation of Hispanic and Asian populations, relative to our community. Those imbalances were partly addressed by weighting our sample population by zip code, race, and sex to match the county. We did not account for age imbalance in our sample, and could not ascertain representativeness of SARS-CoV-2 antibodies in homeless populations. Other biases, such as bias favoring individuals in good health capable of attending our testing sites, or bias favoring those with prior COVID-like illnesses seeking antibody confirmation are also possible. The overall effect of such biases is hard to ascertain."
In the south bay? Pretty good, unless you want to argue for a demographic skew because of Facebook's poor uptake among iOS users.
I mean, no. It's not perfect. It will miss demographics like the elderly with lower social media use, but that group tends to be well-sampled already due to their risk profile. It will probably miss some immigrants too, which seems like a bigger problem.
But really, it's a pandemic. It doesn't care about your socioeconomic status. One of its defining qualities is the extent to which it does not cluster in particular communities like more typical epidemics.
They also were unable to remove any bias towards people self-selecting to be part of the test because they felt they had symptoms of COVID. The bay area has been in lock down since early March, its really hard to imagine someone participating if they didn't feel they had some symptoms and wanted to 'know for sure'.
I'm much more concerned about selection bias toward prior sick people; IIRC, Stanford offered to report positive results to the patient.