Detergents are polar substances that bond with combustion byproducts and also provide a reserve alkalinity to neutralize the acids formed during combustion.
As a marine gear doesn't produce any combustion byproducts, it probably doesn't require detergents. Detergents may foam in some gearboxes and entrain air between the gears (or friction plates?), decreasing the boundary lubrication.
Foaming is a function of speed and temperature (and probably vapour pressure and viscosity, but don't really know or remember), so it may or may not be an issue in your gear. Observe the bullseye under various load conditions.
If the manufacturer recommends it, it may be a good idea to run non-detergent; and if that is the case, why wouldn't you?
IIRC, the AGMA, had switching to non-detergent oil as a recommendation for foaming troubleshooting. I can look that up in the morning when I have access to my reference material.
Edit: Foaming itself may not have to much to do with the detergents in no detergent oil, but more with the quality of the base oil used. Some foaming is normal in gearboxes, often you can see bubbles collapsing on the surface. It is the micro bubbles that lighten the color of the oil itself with entrained air that is harmful.
By the way, thus information is just (very) basic tribology information gleaned from my life in heavy industry. It may or may not be relevant to your specific application. However, it may support why Twin Disc recommended non-detergent oil.
Edit (again): I just looked at a few exploded diagrams of Twin Discs, and it may not have anything to do with foaming at all, but perhaps the amount of fine splines, and the tendency for detergents to bond to metal parts, possibly "gumming up" the internals and not allowing, or slowing the engagements of the clutch, leading to more wear. I'm intrigued. Maybe I'll call them myself, as I can't find anything in their published manuals recommending non-detergent oil, but much anecdotal information about TwinDisc engineers recommending non detergent oil.
Either that or RickB will come along, slap my peepee, and provide the correct information in the morning...