Check content of EEPROM during run-time like Visual Studio
Yes, you can view the EEPROM during debugging. Here's the warning window in MPLAB: 



And the EEPROM memory view for your current processor: 



Edit: 

Given your described symptoms, there are two main possibilities. 


You are not writing the EEPROM properly- some problem with your code, such as not setting the WREN bit. 
The debugger is unable to read the EEPROM memory because you have enabled code protection.