Are ionic solutes always soluble in water?
There can be; of course, it depends on the identity of the species that is dissolved.
Ionic substances generally have some solubility in water, because water is an excellent solvent to separate and stabilize the solute ions. On the other hand, I could quote many insoluble ionic solutes, i.e. phosphates, carbonates, sulfides, where the ionic bond is too strong to allow water solvation.
Purely covalent compounds, for instance alkanes and alkenes, would have little water solubility. Smaller alcohols, ethanol and methanol, are infinitely miscible (i.e. soluble in any proportion) in water, due to the hydroxyl group, which gives water like properties. For longer alcohols, i.e. propanol, butanol, etc. water solubility becomes limited, as water cannot effectively solvate the alkyl chain.