Offspring of whites will all receive a recessive white gene from each white parent. They could receive one from a non-white parent if that parent carries it. This is why whites occasionally pop up in a colour flock unexpectedly. When present in only one copy, there is no way of knowing it is present in a bird unless you know the genetic backfground of the bird (such as one parent being white).
Partridge is not recessive...exactly. Partridge is e^b plus Pg. Pg is dominant; e^b, while it is the most recessive E-allele (usually, in certain cases E^Wh is more recessive), it is the E-allele found in almost all silkies.
The whites may carry Pg, or may not, there is no way of knowing. Chances are pretty high that they are e^b. The other varieties, especially newer and project varieties are the ones more likely to carry different E-alleles, due to cross breeding to bring in various genes.