The bottom line is to do what you like best!
I believe that using level wind reels are much easier to control with downrigger fishing than spinning reels. I took a friend of mine fishing a few months ago and when I let his line down with the clicker on, he started yelling at me to turn it of because I would wear it out. I told him to buy good equipment and he wouldn't have that problem. Depending on the equipment you have, the clicker may be made of plastic which may wear faster than a metal one. Now, during the off-season would be a great time to go over your equipment and look for any damage or wear. I personally send my rigs down with rod in hand, freespooling with thumb on the spool for backlash control. I need to crank down on the final rod bend anyway. Once I have my drag set on the sweet spot, I don't like messing with it.
I too use the ambassedeur reels and was extremely impressed that I could still get replacement parts for my 30 year old reel direct from the company. If you are setting your rigs without rod in hand, do what works best for you.