Hydrogen bonding in complex compounds?
In the generality the question cannot be answered with a definititve statement. You have to look at the cases. For example in the solid state structure  of CuSO$_4\cdot$5 H$_2$O, which is actually more like [CuSO$_4$(H$_2$O)$_4$]$\cdot$H$_2$O, the single crystal water (non-coordinating water) in deed forms hydrogen bonds to oxygen molecules of other coordinating water molecules. In general one could maybe predict, that coordinating water molecules for steric reasons are less likely forming hydrogen bonds to other coordinating water molecules: The oxygen points to the metal and the protons will point to outside so the likelihood of protons from coordinating water molecules  meeting oxygens of coordinating water molecules is small.