Yes, the Nikon F is 147mm wide (I measured one).
I have never had an S3, but looking at pictures, there are some body differences. The wind/shutter controls are very similar, but the space between them and the rewind knob appears larger on the F. On the underside, the tripod socket for the S3 is centered on the lens axis, but on the F, it's offset to the side by about 1 cm. This would make the back/baseplate not interchangeable even if the width were the same.