I have a (very) simple with regard to the use of Blynk, Arduino Uno and ESP8266. I couldn’t really find a concrete answer on the internet yet.
If I were to connect the ESP8266 to a local network, and then use the Blynk app to change some settings to my Arduino one. For example, change how often a light blinks (twice per minute, instead of once). If I were to now disconnect the WiFI, would the Arduino use the changed settings, so two blinks per minute, and no longer the one blink per second?
The answer is … maybe 
… all depends on how you wrote your code to operate, with and without Blynk server connection.