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Does the water molecules in coordinated water (where water acts as ligand) form hydrogen bonding with other complex molecules? Will the water molecules inside the complex form intramolecular hydrogen bonds?
Consider the examples coordinated water and hydrogen bonded water molecules like $\ce{[Cr(H2O)6]^3+}$ and $\ce{CuSO4.5H2O}$.

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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.

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