ahhhhh the age old question. Actually I think this one is fairly new with the advent of the carbon washer influx that's the norm right now, but the question still remains... Grease or no grease.
Manufacturers have used grease or sometimes even a heavy oil on their washers ever since I can remember. Mostly because the washer material used wouldn't work very well, or last very long, with it. For instance.. a lot of spinning reels come with an oiled felt washer, whether it be on one washer or three. This felt, if left unlubed would burn up with the heat created as a fish takes line. More times than not we'll service an old spinner that's been well used and the drag stack is nothing but metal plates grinding on metal plates! Ouch. Now tell me that the little bits of felt washer stuck to the sides helped stop that fish. I think not. If those same washers were kept oiled up they most likely would have lasted much longer and done their job much better than letting them dry out and keep fishing.
Same goes for cloth washers like in some lever drag reels and older Shimano baitcasters. The cloth would just burn (or turn color from the heat) and the drag would be jerky. Now put some drag grease on them and that changes everything. The drag now becomes better at startup and remains smooth through the entire drag range. Same with a lot of these so-called proprietary black washers, whatever they may be called. If they are left unlubed or let dry out, the drag becomes jerky and unresponsive with the end result being the washers overheating, and ultimately cracking and ending up all over the inside of your reel. A nice yummy mess.
Now take the carbon washers of today, can be used either dry OR greased. These washers DO NOT BURN. Try to light one of these with a lighter and nothing happens. Carbon doesn't burn up like the other types of washers and they don't seem to change with a long fish fight. (No fade or very little) When these washers are installed dry and in a CLEAN ENVIRONMENT (no old oil or grease, dirt, etc) they are exceptionally smooth and deliver a fantastic range. This is even more apparent in multi-disk drag stacks like (for example) an Abu 6500C3 or Daiwa Luna 300 or Shimano Calcutta 400. When greased washers are installed in the very same reels, one would think that the drag either becomes non existant or better depending on which side of the fence you come from. Fact is that the drag still has a pretty good range but has a lighter startup in light drag settings. The greased drag in these multi disk reels works very similar to a non greased setup other than the extreme top end (max drag pressure). The maximum drag tension is lessened to a degree with the grease. Makes sense too....grease on your car's brakes may work but an extreme stop just won't happen.
In a single drag disk setup, say for example a Shimano Curado 200, a dry carbon washer seems to be not quite strong enough to satisfy the status quo. Grease it and the max drag gets better. Go figure.
In a saltwater setup, I wouldn't even hesitate to grease the carbon washers. This extra grease will aid in fighting off the ever corrosive saltwater and keep the washers from drying out and collecting salt air moisture in them, causing the drag to become jerky.
Hope we shed a bit of light on this subject, now it's up to you to choose :)