Are you talking about the Oath-Breaker Paladin? If so, the answer is yes, they are paladin sub-class and so get all the features common to paladins in addition to the features granted by their sub-class.
If you mean the Death Knight monster, on the other hand: no. They already have a version of Divine Smite built into their attack (which deals 1d8+5 slashing plus 4d8 necrotic damage), but they can't sacrifice spell slots directly to deal more damage without using one of their smite spells (e.g. searing smite).