They almost certainly will not encode any explicit biases of the algorithm authors (e.g. “she’s pregnant, can we get rid of her?”), which is already a great step forward, as explicit bias is still sadly far too common in the workplace.
When implicit biases find their way into algorithms, it is usually a specific edge case that’s a function of the training data (e.g. facial recognition preforming poorly on darker skinned people due to training set imbalance). The biggest case of implicit bias in algorithms I’m aware of is when the training set is the behavior of society as a whole, as with search engines: for example, women search less for C-level jobs and so are less likely to be shown postings for C-level jobs when doing job searches (thereby perpetuating a vicious cycle), or websites depicting Black teens are more likely to show them in a criminal context than White teens, so searches for “black teenager” show pictures of criminals whereas searches for “white teenager” do not.
These implicit biases are not encoded by the algorithm developer but rather by the dataset the algorithm is applied to.
In the case of automated firing, I don’t see how implicit bias can creep in if the metrics are strictly work-related (e.g. fraction of on-time deliveries). For the record, I do not agree with automating performance metrics, since they cannot account for nuance (e.g. delivery drivers assigned to gated communities have issues opening the gate and thus deliver fewer on-time packages, which is not accounted for in the algorithm.) However, this is not a form of demographic bias, explicit or implicit.