If I pack all the textures the file size of the blend file can grow substantially. How will this influence the render performance ? Does GPU/CPU rendering make a difference ?
.blend file size does not influence render times. Does not matter if render engine load packed data from .blend file or from folder. Here can be difference in milliseconds only on beginning while Blender preparing scene. Not while render it.
Difference between CPU/GPU: Of course there are difference in speed as well as final render output. If you ask for difference about preparing scene, here can be differences in millisecond too. Render engine need move data to your graphics card and this need a time. But don't worry about it, 4GB VRAM in graphics card can be filled in a split second. If we consider that GPU can render much faster than CPU this is absolutely insignificant. Of course, all depend of PC specs- This is true for "balanced" systems, not for system with extremely powerful CPU and low end office graphics card.
In some cases image rendered using CPU can be different as rendered using GPU. Not always, usually if you use volume and/or SS shaders. Some of this differences was eliminated in Blender 2.78, but nobody know if everything is OK now. The time will show :-)