Does hydrogen bonding contribute in solubility of a substance
Ethoxyethane, better known as "diethyl ether" or even just "ether", can form hydrogen bonds with water.  But fitting the ether molecules into the water solvent means you have to break up some water-water hydrogen bonds, and the ether molecules cannot replace enough of those hydrogen bonds to dissolve freely.

Of course, ether does form some hydrogen bonds, which makes is more soluble than it would be without the hydrogen bonds (compare ether with, for example, diethyl sulfide).  But most (or at least the most common) freely water-soluble organic compounds have either ions to generate ion-dipole interactions with the water, or hydroxyl groups that readily fit with the hydrogen bonding structure of the water (think of ethanol or sugars).