Is it possible to run referenced model in External Mode?

I would like to use External Mode in Simulink. In the top model there are referenced models. I am able to generate and run the code. However, the changes made in the referenced model are not propagated to the top model when running in External Mode. Is it possible to run the referenced model in External Mode?

I enclose a toy-problem as an example. The issue is that changing the value of the Gain block inside the referenced model does not affect the value displayed in the Scope in the top-level model. To run the example, one needs to "run_before_simulink.m", then open the "toy_top.mdl" and click "build button" in Simulink. The run the created "toy_top.exe" and click "connect" in the top bar. One can see that changing the value of the "Gain" does not affect the content of the Scope. Is it possible to make this change propageted to the top model?

If not, I would be grateful for looking at my other two questions:

Why "Initializing" step during code generation from Simulink model takes so long? - MATLAB Answers - MATLAB Central (mathworks.com)

Is it possible to autmaticly switch between referenced model and subsystem in Simulink? - MATLAB Answers - MATLAB Central (mathworks.com)