It will not, I specifically included the F-stops for that reason.
The depth of field is determined by the focus distance and the aperture of the lens. Both remain unchanged.
Note that 35mm F/2.0 is the same aperture as 70mm F/4.0. Both lenses have an aperture of 17.5mm. (35/2.0 == 70/4.0)
You can easily verify this with your favorite zoom lens. If you have an 24-70 F/2.8 available to you, you can verify by taking 2 pictures; one at 35mm F/2.8 and one at 70mm F/5.6. Crop the 35mm one to 25% area (half the width, half the height). Render both images to the same size (print, fill screen, whatever) and see for yourself.
