You have not clarified what you meen by “Client App”, but if referring to the Blynk App on your phone, simply don’t click on the App icon until you know the server is up The Server IS the master of the App, so the App knows nothing, can do nothing, is nothing, without the Server to log into.
But if you are referring to a Blynk Client (AKA some form of code running on an MCU of some sort), then you can code it in such a way as to run without the server if needed…
The Server IS the master of the App, so the App knows nothing, can do nothing, is nothing, without the Server to log into.