Algorithms which are both deterministic and non-deterministic
First of all, your terminology is at odds with computability and complexity theory. What you are asking is whether it makes sense for an algorithm to have both randomized and non-randomized components. A good example are algorithms which have to be unpredictable (say for cryptographic reasons), but for the purpose of testing have to be predictable. In this case, we substitute a pseudorandom number generator for the true (say, physical) random number generator for testing purposes.

That said, the class of algorithms you are describing are just randomized algorithms. Nothing forces a randomized algorithm to use randomization, it's just a possibility in the model, in the same way that a non-deterministic Turing machine can be deterministic, or that a real number can be rational.