Causal effect estimation is critical to a range of scientific disciplines. Existing methods for this task either require interventional data, knowledge about the ground-truth causal graph, or rely on assumptions such as unconfoundedness, restricting their applicability in real-world settings. In the domain of tabular machine learning, Prior-data fitted networks (PFNs) have achieved state-of-the-art predictive performance, having been pre-trained on synthetic causal data to solve tabular prediction problems via in-context learning. To assess whether this can be transferred to the problem of causal effect estimation, we pre-train PFNs on synthetic data drawn from a wide variety of causal structures, including interventions, to predict interventional outcomes given observational data. Through extensive experiments in synthetic and semi-synthetic settings, we show that our approach allows for the accurate estimation of causal effects without knowledge of the underlying causal graph.