Yes, that cross would produce sexlinked chicks. The mother would pass barring only to her sons and not to her daughters, meaning male chicks will have a head spot and female chicks will not.
The breed of the father in that type of cross does not matter, as long as he is neither barred nor solid white. A barred rooster will indiscriminately pass the barring gene to both his sons and his daughters, thus making it impossible to be sure which is which. A white rooster can have one of two effects on the cross; either he is dominant white and passes this on to his offspring, making it difficult to determine which are barred and which aren't, or he is recessive white and might be hiding genes that would make the cross ineffective for producing sexlinked chicks.
As a side note, the light skin of the OEGB or Plymouth Rock bantam is also sexlinked! When crossed to a dark-skinned breed like a Silkie, this makes a skin color sexlink cross where male chicks have light shanks like their mother and female chicks have dark shanks like their father. So you should end up with barred light-skinned males, and non-barred dark-skinned females from this cross.
