Interrupted survey designs compare respondents interviewed before and after unexpected events to identify causal effects. When pre-event and post-event samples differ in their covariate distributions, researchers must adjust for these imbalances. Common approaches such as regression, reweighting, and matching require specifying which functions of covariates matter for adjustment. If the true relationship between covariates and outcomes involves nonlinearities the researcher cannot anticipate, bias remains even after adjustment. We propose Gaussian Process (GP) regression as an alternative that learns the conditional expectation function from pre-event data and applies it to post-event units, adjusting for smooth nonlinear functions of covariates without explicit specification. When covariate overlap fails—common when sequential fieldwork leaves some regions with only post-event respondents—GP produces conservative estimates with appropriately widened uncertainty rather than confidently extrapolating. Simulations demonstrate that GP achieves the lowest RMSE under standard conditions and maintains stable performance under non-overlap, where conventional methods exhibit increasing bias. Replication of four published studies confirms these properties empirically, with GP estimates diverging from conventional approaches precisely where overlap is poorest.