No, the RAM space of 256 bytes is not sufficient in the boot loader project. Therefore it is mandatory to enable paging for making boot loader operational.
When paging is disabled, the device will act as a single RAM page device implying that only 256byte RAM is available for use. This memory will be shared by Global Variables as well as Stack.
Now let us say that out of the 256 bytes available:
Global Variables used 120bytes.
RAM required for boot loader variables is 49bytes.
If EEPROM module used, 8 bytes will be used up.
Therefore, about 80 bytes are available for stack.
For writing to flash in 64byte block, the boot loader will consume 64bytes of RAM for each write. Moreover after entering the boot loader a large stack area is needed.
The amount of stack required is very difficult to predict.There will be nested function calls as well as interrupts might be serviced. Therefore a large stack will be required.