Because I was really curious about this, I decided to do an experiment:
One of these shots is with a TP over the flash head, one is not. I had to do this with an external flash because even in manual mode, it appears that my Canon DSLR automatically adjusts the built-in flash
I found that a piece of TP was worth about 3.3 stops of light. Because my flash is only adjustable in 1 stop increments, I had to adjust the f-stop slightly to get similar exposures. I white balanced both techniques separately. I shot off camera at a 30 degree angle in order to show shadow edges.
No editing was done except for a crop and a very slight raising of the exposure on one shot to get them even closer together in overall exposure.
Settings were
ISO 200
1/200"
30mm
With TP:
f/8
Flash at 1/16 power, 24mm
Without:
f/9
Flash at 1/2 power, 24mm
The flash was approximately 3 feet from the subject, 30 degrees to camera right
What I did notice, which is expected on an external flash especially, is that the paper acted to increase the area of coverage slightly, but did not alter the softness of the light much at all - were the flash moved back even more, the edges would become indecipherable between the two.