So is it in general safe to say that the less "insoluble" a precipitated compound, the lower the yield is likely to be for that precipitation reaction?
Yes, although below some level of solubility you will not see any effects. Imagine you are trying to precipitate 1 gram of substance from 1L of solution. CaSO
4 is considered insoluble, but the saturated solution is 0.005M - almost 0.7g per liter. AgCl is considered insoluble as well - saturated solution is about 10
-5M, so you loose about 1.4 mg per liter. AgI is even less soluble - something like 10
-9M - so you loose around 2*10
-7g. From practical standpoint both AgI and AgCl are completely insoluble when it comes to collecting precipitate, which can't be said about CaSO
4.
Note - I am too lazy to check exact numbers, so I can be slightly off, especially with AgI.