Yes, on both counts. The bombing of Rome had been a possibility from the start of the war, in 1940 and 1941 the Air Ministry considered launching raids from Malta in retaliation for Italian bombing of Athens or Cairo, but demurred due to concerns over heavier reprisals and the status of Rome and the Vatican. Pressure to bomb steadily increased over 1943 as the North African campaign concluded and the Allies turned their attention to an invasion of Italy, but not without considerable debate on political, cultural and religious grounds; Churchill had no objections, but Roosevelt had to consider forthcoming elections with substantial numbers of Italian-American and other Catholic voters. The Archbishop of Canterbury wrote to the Secretary of State for Air asking for Rome to be spared but Sinclair replied that military objectives must be hit regardless of their proximity to old buildings. Charles Portal, Chief of the Air Staff, was in favour, though he noted that some of his crews were reluctant to bomb targets in cultural cities including Rome, Florence and Venice; Anthony Eden and the Foreign Office were opposed on political grounds.
As the Allies prepared for Operation Husky, the invasion of Sicily, Eisenhower's headquarters identified two rail marshalling yards in Rome important for moving German reinforcements and sought permission to bomb them. Churchill and his Cabinet "had no hesitation in supporting the proposal" and cabled Roosevelt on June 10th 1943, who was "wholly in agreement as to the military necessity of interfering with railroad communications".
The Catholic Church, up to and including the Pope, appealed to the Allies; see "Appeals of the Vatican to the American and British Governments that they refrain from bombing Rome" in Foreign Relations of the United States: Diplomatic Papers, 1943, Europe, Volume II for communications including Pope Pius XII to President Roosevelt in May 1943; Roosevelt's reply of June 16th, following his telegrams with Churchill, stated that "In the event it should be found militarily necessary for Allied planes to operate over Rome our aviators are thoroughly informed as to the location of the Vatican and have been specifically instructed to prevent bombs from falling within the Vatican City. This may be an opportune time to warn Your Holiness that I have no reason to feel assured that Axis planes would not make an opportunity to bomb Vatican City with the purpose of charging Allied planes with the outrages they themselves had committed."
Leaflets were dropped on July 18th 1943 warning of the attack, which followed on the 19th, led by Jimmy Doolittle (of the eponymous raid on Tokyo) who offered Catholic pilots the opportunity to step down, though none did. Crew were briefed in detail with the strictest instruction to avoid four Major Basilicas including the Basilica of St. Peter in the Vatican; they were able to do so, but the Basilica of San Lorenzo, in close proximity to one of the marshalling yards, was not marked on maps to be avoided and was hit during the raid and seriously damaged.
Roosevelt had received correspondence from the Pope asking him to declare Rome a free city, and was very concerned on how bombing the Vatican would play with Catholic voters. Hap Arnold was also concerned about how it would be construed among the numerous Catholic airmen in his command. The initial target in Rome was the train yards in the San Lorenzo district, because this was the most important military target for the Allies and the Tiber served as a very distinct geographical landmark to help avoid mistakes.
"One of the hottest potatoes I had to handle during the war was the mission of our bombers in support of the Allied troops moving up through Italy," Arnold wrote in his memoirs.
We had finally come to the conclusion that if our bombers could cut the railroads running north and south in Italy, all supplies to [General Field Marshal Albert] Kesselring's [German armies in Italy] would be stopped. Then had arisen the question of bombing the marshaling yard in Rome. Through the President and the Secretary of War; influences from all sides were brought to bear to prevent me from bombing Rome. I told them I was confident we could hit the railroad yard, destroy it, and thus cut that last link between north and south Italy without damaging a single church. If we destroyed that yard it would be impossible for Kesselring's army to receive any supplies except by road, and I was convinced that our light bombers and fighters could take care of the road traffic. Finally, very reluctantly, we were given the necessary authority.
From Hap Arnold: Inventing the Air Force. Bill Yenne.