No
What do you think the value of count will be after
for (int i = 0 ; i < EEPROM.length() ; i++)
{
EEPROM.write(i, 0);
}
count = EEPROM.read(COUNT_ADDR);
Apart from any other problem (there is at least one), count is an int and needs 2 bytes of storage but EEPROM.write() and EEPROM.read() only write and read a single byte