I think MAD only can be used to detect anomalies for time series without a trend because it relies only a stable median to detect anomalies. It should be OK for time series with seasonality. Just seek confirmation here. This question is limited to when MAD is used as a standalone algorithm without coupling with other methods for anomaly detection.
MAD definition and use:
Suppose we have a set of observations: $(x_1,...,x_n)$
$$Median = median(x_1,...,x_n)$$ $$MAD = median(|x_1- Median|, |x_2- Median|,...,|x_n- Median|)$$
Then we can use $Median$ +/- 3*$MAD$ as thresholds to detect anomalies.