No, it won't. Consumption plan by default will scale your function app based on demand. By switching to the Premium SKU, this is a decision you will have to make based on your application needs. This warning message is just to alert you that your app has not been configured for scaling yet. Things you will want to check are:
App Settings: Ensure that your app settings are configured to support dynamic scaling. This might include settings related to instance count, scaling rules, and other parameters that control how your app scales.
Code Configuration: Make sure your code is designed to handle scaling events. This includes handling state management, session persistence, and other factors that might be affected by scaling.
Monitoring and Alerts: Set up monitoring and alerts to track the performance and scaling behavior of your app. This will help you identify any issues and make necessary adjustments.