Are more classes more favorable than a single combined class? Imagine the following scenario.

Train a classifier that classifies an object into one of these n+m classes:

class 1..n     -&gt; triggers an action A depending on the predicted class p
class n+1..n+m -&gt; triggers an action X independent on the prediction


Used is the CalibratedClassifierCV of a LinearSVC of scikit-learn. So, the prediction is based on the maximum predict_proba value.

Question

Because action X is independent on the prediction, I would very like to combine the m classes (n+1, n+2, ..., n+m) into a single class (to improve training speed, classification speed, memory consumption etc.)

Would that harm the classification result?
So what you are interested in (in terms of prediction) is $n+1$ classes, where the last class is $m=1$. This would be my default model. In other words, I don‘t see why you should have $m$ additional outcomes if these outcomes are irrelevant for your task. 

For the quality of a prediction, features $X$ matter the most. I‘m not aware that the classes are relevant unlike your outcome (=classes) have an order. 

However, ultimately you need to test which model performs best. So by the parsimony principle, start with a simple model and gradually see if adding complexity delivers a better result (by a predefined measure such as accuracy).