Direct answer: No, you must not exhale. You need to keep that breath for the whole descent — it is both your fuel for the ascent and your buoyancy.
Why is exhaling so dangerous? The deeper you go, the more the gas in your lungs is compressed. If you exhale at depth, you are dumping the little oxygen reserve you have left; and because your lung volume drops sharply, your lungs fall below the safe limit at a much shallower depth, which greatly increases the chance of a squeeze injury at depth — then, as you ascend and the gas expands again, already damaged lung tissue is stretched further.
- Keep the glottis closed during the descent. Hold that breath until the ascent is finished and you are close to the surface, then exhale for recovery breathing. Do not let out even "a little bit" in between.
- Equalize using the air in your mouth. Frenzel or Mouthfill relies on control of the mouth and soft palate, not on exhaling air from your lungs.
- If you cannot control it, ascend. The urge to breathe does not mean you are out of oxygen, but if you can no longer hold back the urge to exhale, that is a sign this descent should end.
In one sentence: this breath is a return ticket you cannot tear up. These actions must be practised under the guidance of a certified instructor, and every dive must be watched by a buddy with rescue skills; after surfacing, your buddy must observe you for at least 30 seconds following the surface protocol. Testing "whether I can exhale" on your own is the easiest way to get into trouble.