No it doesn’t.
First of all, when you say “double the shutter speed” I assume you mean double the amount of time the shutter remains open. That is what happens when you switch from 1/250 sec. to 1/125 sec. Since 1/125 sec. is twice as long a time period as 1/250 sec., the shutter remains open for twice the amount of time, thus allowing twice the amount of light to reach the film (or CCD, or CMOS, or what have you).
Switching from f/4 to f/2.8 is stopping up not down. f/2.8 represents an aperture with a diameter twice the size of that which is represented by f/4, and therefore allows twice the amount of light to reach the film (or CCD, or blah blah blah).
So, in your example, what you’ve done is created a larger opening for the light to travel through (thus, more light gets through) and allowed the light to travel through that opening for a longer period of time (thus, even more light gets through). So things don’t balance out nicely. You’ve just over exposed that one in a million shot of Elvis sipping tea with two aliens in a Paris bistro by two stops or 4 times too much light!
You and I both know what you meant though. You can half the amount of light with one function and double it with the other and things will balance out nicely. In other words, a setting of 1/250 @ f/4 will yield the same exposure as a setting of 1/125 @ f/5.6.