Did you even check how much EEPROM the chip's got on board? Check the datasheet.
The MCP4725 device has a 14-bit wide EEPROM
memory to store configuration bit (2 bits) and DAC
input data (12 bits)
The only reason for that EEPROM is so that the chip can maintain it's settings through a power loss. It only stores one output value, not a waveform's worth.
The answer is no.