EF lenses are designed to work in cameras with 24x36mm sensor, which we call full frame, and also in smaller sensors, as APS-C.
On the other hand, EF-S lenses will not work at full frame bodies. Sigma DC lens, equivalent to the Canon EF-S, and are designed only for APS-C bodies, but also fit the EF bayonet, but will have image with the dark corners in full frame.
When you say EF-S lenses "will not work" on full frame bodies.. can you expand on that? Will they physically not fit?
Again, it was my understanding that the EF mount was universal.