That is, if the substance has a high specific heat, will it also have a high boiling point? ( and vice versa)
According to the Ehrenfest classification, during a first-order transition (such as boiling) the heat capacity $C$ goes to infinity. This makes sense, since at the transition point the temperature does not change with input of heat and $C = dQ/dT $. This and other considerations add a little complexity to the problem, as it requires you to state which heat capacity (at which T) you are talking about.
More importantly, however, the boiling point depends on the magnitude of attractive intermolecular forces compared to kT, whereas the heat capacity depends on all the available degrees of freedom (including intramolecular). Therefore you can envision large and small molecules with similar overall solution composition (for instance hydrocarbons) - and thus similar heat capacities - but very different BPs. See for instance this table of specific heats, where C for hexane through dodecane are very similar, whereas their BPs differ quite a bit.