If you have 2-stage clutch, it's still "live".
Single stage clutches are not "live".
However, the blades on a rotary cutter have a lot of inertia due to the weight. My cutter, a 60" Land Pride, takes darn near a minute to spin down even when the PTO is disengaged.
Depressing the clutch long enough to shift gears (even in a non-synchro transmission) won't even slow your cutter down enough to be of any concern.
One thing you do want to consider is that cutter "driving" your tractor when the clutch is depressed. You'll want an overrunning clutch installed on the cutter's drive line.
As far as loader work, the difference in time (if any difference), might be a second or so. I doubt if most HST owners have enough experience with gears to be knowledgeable on the subject. However, I would caution against inexperienced or multiple operators using a gear transmission. Clutches are tough and long lasting, but abuse can really cut their life down.