No, you will not get a wider angle of view by using the Speed Booster. With the Speed Booster, your NEX acts like it has a full frame sensor. You must use full frame lenses with the speed booster in order to not vignette.
As it is essentially full frame, you have to treat it as such when selecting a lens to use.
For example: with a KOWA on the NEX camera without Speed Booster, the widest lens useable without any vignetting is probably around 45mm.
On the same NEX with Speed Booster, you must treat it like a full frame camera. The widest lens useable without any vignetting is around 75mm.
Because of the effective "sensor size" difference, these two lenses have pretty much the same field of view (even though they are different focal lengths). So the 58mm Helios, while great an NEX without the Speed Booster, would certainly vignette with the Kowa, just as it would on your 5DII. As itimjim says, treat it like a full frame EOS-mount camera when the Speed Booster is on . . . use 75/85mm and beyond lenses.
The difference is one of light intake and depth of field. As essentially a full frame converter unit, the Speed Booster brings full frame-equivalent shallow depth of field to the NEX cameras. Because it shrinks a full frame image circle to the size of an APSC sensor, the light is also brighter, giving you an extra stop (can't remember exactly how much extra, but it is a fair bit).