Yes, you would either generate Stan code or rewrite your AST into something the Stan compiler understands.
However, if Church allows you to express non differentiable models (e.g. if you have a Heaviside function), then they will either fail or not work well with HMC or ADVI (the variational inference algorithm Stan uses), because both assume that gradient of the posterior can be computed and is informative about the posterior.
However, if Church allows you to express non differentiable models (e.g. if you have a Heaviside function), then they will either fail or not work well with HMC or ADVI (the variational inference algorithm Stan uses), because both assume that gradient of the posterior can be computed and is informative about the posterior.