As far as I know, no, you really can't do something like that.
This is because RAM almost always needs to be accessed very quickly, and FLASH/EEPROM is very slow to write. Also, FLASH/EEPROM has a number of cycles before it wears out and breaks down. So even if you could get it to work with the speeds, you would burn out the chip right quickly.
Now there *COULD* be some kind of single hybrid RAM/FLASH chip floating around that was designed for doing exactly what you are talking about. But I wouldn't know what it would be called or where to get one. Maybe someone else does?
Edit: As stated below, there could be some other kind of bleeding edge SiFi chips out there that can give you your cake and let you eat it too, but with specifically FLASH or EEPROM physics... no, it can't really be done that I am aware of. Two entirely different intended applications.