As Jome mentioned, it seems that you would get a better training stimulus by training without hyperventilation but I also think it can be beneficial to do some training with hyperventilation.
The reason being that you would want to simulate your maximum breath holds as much as possible, and if those are usually done with hyperventilation you will be more familiar with the way your body responds in that case, keep in mind that I am not that experienced. Maybe I see it this way because I have not experimented that much with hyperventilation and the first time I tried purge breaths this summer I had a near blackout. Fortunately I had experienced buddies who removed my mask and shortly after I start breathing again.
Since then I have been doing 2 to 3 minutes of deep breaths (2 sec. inhale, 12-14 sec. exhale) and a few purge breaths before the hold and I am much more comfortable that I was at first. By the way, I'm not sure that is considered hyperventilating so what I mentioned might be off topic.
anyways, just my 2 cents.
Daniel