It certainly wouldn't hurt them.
WD-40 was designed specifically to be a water dispersant -- SEE:
http://www.wd40.com/ -- but it also frees stuck parts, such as frozen gears, etc. I've used it to do a cursory cleaning, prior to taking down the motor, to make sure everything winds down completely.
For cleaning and re-greasing the spring barrels, I'd follow the steps outlined in the Compleat Talking Machine. The Credenza was fitted with the four-spring motor, with two coiled springs contained in each of the two barrels. To remove the barrels from the rod or shaft, you have to, first of all, unscrew the small set screw (or screws) which holds the shaft in place. Then, carefully holding onto--or stabilizing--both barrels, slide the shaft out. (Normally, a few whacks on the end of the shaft using a long screw driver and hammer will move it far enough to clear the hole, so that it can be pulled out.
After the barrels are removed--and make sure to note which one goes where--you have to pry out the round end-cap retaining spring on each barrel, in order to remove the end-caps. Once done, the top spring in each barrel is exposed.
A few collectors I know have insisted that it is not necessary to remove the coiled springs in order to clean them properly. Instead, they advise soaking each barrel--springs and all--in kerosene overnight, then allowing each barrel to drain for a few hours, and dry. They then apply about three tablespoons worth of grease onto each exposed spring, replace the cap and retaining spring--and then work about 1/2 cup's worth of grease into the hole of the opposite (sealed) side of the barrel, so the second (bottom) spring is also lubricated.
As for the turntable speeding up or slowing down, in addition to gunked up gears and mainsprings, another cause could be an improperly seated governor. As you can see, the governor is held in its position by a bearing on either side. Each bearing is held in place by a small locking screw. After the motor is completely run down, try moving the governor back and forth along its mounting. If there is noticeable movement, loosen the retaining screw on the "inner" side of the governor--the one near the long "spindle gear" and push the bearing inward toward the governor until it just stops, and tighten the screw. Test the governor by spinning it. It should spin freely, but with no sideways movement. (While doing this, make sure that the outer governor bearing is also held firmly in place by the screw. If not, tighten the screw.)
When inspecting the governor, make sure that the flat springs connected to the round weights are not loose. If they are, GENTLY tighten the screws holding them. (Too much force could break the flat-springs.)
Hope some of this made sense.
Joe_DS