No, it doesn't.
Sadly, it doesn't work, it will still have the same x2 steps off of hatching the egg.
However, I suggest you use the Hatching O-Powers, as they can help quite a bit.
Hatching O-Power Lv.1 shortens the time by 1.25x
Hatching O-Power Lv.2 shortens the time by 1.5x
Hatching O-Power Lv.3 shortens the time by 2x
So, if you have Hatching O-Power Lv.3 activated, you can have the effects of two flame bodies for the price of one flame body in your barty!
Hope I helped!
My giant brain!