You seem to be confusing things here. The basic small open economy model is non-stationary, but it has nothing to do with growth where writing everything in intensive form removes the unit root. Rather, the model features a unit root because not foreign assets are non-stationary. It is basically the permanent income hypothesis at work. If there is a change in foreign bonds, agents will always consume the annuity out of these additional savings, but they will not consume more than that. Hence, bonds stay at their new level and never return. This is why you need to use one of the tricks available to make the model stationary. See e.g. the reference at [Closing Small Open Economy with Debt elastic interest rate)