Ceiling is one aspect of flying, visibility is another. If the ceiling is low, visibility is also going to be low
Certainly in an emergency, highly skilled pilots could operate with limited effectiveness under such conditions but typical pilots would suffer needlessly high casualties and be at high risk of inflicting/receiving blue on blue casualties. Remember, if allied aircraft attacked allied ground forces, allied AA crews were under shoot to kill orders and AA crews would be credited with such "blue" kills.
At 250mph, an airplane is moving 366 feet per second. If visibility is 2,000 feet, the pilot has just 5.5 seconds from the moment he spots a potential target dead ahead until his plane is directly above it. His time to spot a target to either side of his plane is even less. All this time he needs to maintain an awareness of where he is at by visually identifying landmarks, something not easily done under adverse weather conditions during combat operations.
Let's not forget that he is part of a flight of aircraft so he must continually maintain awareness as to where his other aircraft are.
Assuming they happen upon a nice target, ground attack aircraft like to attack in such a way as to avoid concentrated ground fire. This means the planes must disperse and try to attack more or less simultaneously from different compass points. Difficult to do at 250 mph under low ceiling and visibility.
Perhaps the pilots could slow down to say 125 mph. Doing so will double the time they have to search for targets, maintain orientation and flight position. However, if they are flying at 1,000 feet at 125 mph, they will be extremely vulnerable to small arms fire. The overcast conditions will enable 8mm tracers to burn brightly and quickly fade upon entering the clouds just above the aircraft. This rapid fading of tracers in the clouds makes aiming easier because bullets that traveled beyond the aircraft quickly disappear from view. An altitude of 1,000 feet is just 330 yards which is well within lethal range of 8mm bullets, thousands and thousands of which will be coming up at the planes. Actually, going so slow and low over enemy territory could be expected to draw continuous small arms fire. Yes, the planes had some armor protection but not that much.
So, the best course of action under such weather conditions would be to just leave the planes parked, give the pilots a rest and aircrews time to do needed maintanance.
And yet...isn't it worth it in some extreme emergencies to put a few pilots at unusual risk to save thousands? The obvious example was Bastogne. There was the need to drop supplies fairly accurately. (I think I recall reading that some such effort was indeed made, though ineffectually.)