This only counts if they recognize you after you return. If they think that you're unique again, then the tracking didn't work at all. This was the case last time I used their tool, Panopticlick.
Edit: I tested this current tool and it recognized me after I returned. Opened it first normally, I'm unique. Opened it in a private window, unique. Closed that and opened a new private window, and bam, one other previous browser had my fingerprint already.
Edit: I tested this current tool and it recognized me after I returned. Opened it first normally, I'm unique. Opened it in a private window, unique. Closed that and opened a new private window, and bam, one other previous browser had my fingerprint already.