Train/Test split or not?

Hi, I have a conceptual question wether I should split my dataset in train/test or not. Given the fact that my dataset has no labels, does it make any sense to split in the first place? I mean, I could simply do something like clf.fit(data) and then get the resulting labels as clf.labels_ and since I train in an unsupervised manner the classifier should not overfit in any way, right?