Can I notate time complexity depending on the result of an algorithm?
You can express algorithms costs in whichever parameters you desire, so long as you define them. The parameters don't even have to be known given the input; that gives your bound limited use, but well.

Warning: Landau bounds are asymptotic, that is they only hold meaning when you let the parameter(s) go towards infinity. That is you can not really use parameters that can not be arbitrarily large.

Warning: It's unlikely that your cost is independent of the input, which is what your bounds seems to suggest. You probably made a mistake.