Jorge Alamañac, thank you for posting this question.
To answer your question - yes, your chatbot (or any other application using the classic Application Insights) would continue to work.
However, there might be specific issues related to unhandled exceptions (which will really depend on the application design). For example, if your chatbot is configured to raise unhandled exception when the telemetry could not be sent to AppInsights, it could crash the application. I would suggest performing a side test using another instance of chatbot configured in current fashion, only this time connect it to a different test AppInsights workspace. Ensure that chatbot functions and then delete the test AppInsights workspace and notice the behavior. This should closely represent the issues that you may face after the migration deadline.
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