That depends, Geo. MN. closed the firearms deer season in 1972, as, there were no deer. If they tried that today, non hunters would overthrow the government in St. Paul due to the damage the deer do to property and cars.
The Federal WMA at Sherburn built an area that was supposed to give people a chance to see Canada geese in a natural state, complete with an observation deck and a pond built for the geese, as someone at the time thought Canadas were the next doomed species. Lets just say that never came to pass, quite the opposite, in fact, and the entire area sits unused to this day. The feds, in my humble opinion, do a piss poor job managing WMAs under their control, and the above is a shining example of that.
Id be willing to bet there are numerous causes in the decline of woodcock and Ruffed Grouse. WNV is likely just part of the puzzle.
Closing part of the season wont likely change anything. Except, maybe, for the goshawks.

Best,
Ted