So your saying I'll have to breed the partridge and penciled back to the parents and then together?Are white rock dom white or recessive white? If they are dom white yes you will get o100% white chicks with spots. If they are recessive WHO KNOWS. The white birds can hide all kinds of stuff, barring, blue, black...... anything could be under there. Most people don't want to cross whites with other colors because of the UNKNOWN. Your barred rock hens should make you sex linked cockerels, unless they are barred under the white.
If you just want to SEE what you get that would be ok, but I think you would have an uphill battle getting something usable out of them. The partridge and penciled rocks patterns will not show the first cross.