No, just the ones inside the scan. The job of collect_deafult_updates is to explain to pytensor how to update random generators inside the scan loop. Since the non_sequence variables are sampled only once, outside the scan, they don’t need to be updated inside the loop.
It looks like the posterior of the AR parameters includes combinations of parameters that induce non-stationary dynamics into the system. You can see this notebook in the Samuelson Multiplier-Accelerator section for some discussion specifically in the context of an AR(2). You can see that the posterior mean gives damped oscillations, but there are explosive oscillations in the tails.
Unsolicited opinion: Your data don’t look like an AR(2) at all. They exhibit strong seasonal behavior, so you should model that first, then consider AR dynamics if it seems like the residuals are still auto-correlated. The model is learning parameter combinations with complex eigenvalues to try to capture the seasonal pattern.