In theory, could I load a VERY small program into the EEPROM, and then, at a certain point in my code, load the program?
Ex.
I run my very complex program until a button is pressed. The arduino then loads this program:
void setup() {}
void loop() {}
(It's my null program, it does nothing and takes up 450bytes of space.)
Why would you want to do that?
In theory, could I load a VERY small program into the EEPROM, and then, at a certain point in my code, load the program?
I never said I did.
It would be completely pointless... In theory you could make a cannon which fired toasters - not a lot of point to it.
You are better off just making them different looping functions and having the button as an interrupt to run some code to switch between them 
Do you just pull these ideas at random out of thin air?
Yes, I did. I pressurized the air in my house and put into a sealed flask with this:
As the air evaporated, the levels were fed from the sensor to my arduino, which output the data as ASCII.
Yes, I did.
Good thing you told us. I was beginning the think you'd pulled them from somewhere else.