Not quite as the Italian and British Navy understood their strengths and weaknesses and tried to get one or the other to commit at a disadvantage that never truly ended up in a decisive fight. After all, the Royal Navy didn't have a real modern answer to the new Littorio Italian BB which had the range and hitting power not to risk some lucky salvos but they would have easily cleaned up the Mediterranean if the Italian Navy only had the 4 rebuild WWI ships to contend with and just modern Heavy Cruisers. Whether it was with more or less Luftwaffe support the Italians were not going to change their naval strategy and suddenly become as risky as the Germans were to send capital ships on convoy raiding missions. This view was further reinforced when they ventured further at Cape Matapan expecting some air cooperation of which where was none and the British had a Carrier. That experience proved that if the Italian Navy wanted to truly run free outside the Italian air umbrella they would have needed at least a Carrier which was sorely needed in that battle seeing as most ships of that era didn't exactly have a good amount of air defense guns on board.
While Cape Matapan was solid Italian loss, it was not the decisive engagement the British were looking for as the Italian navy prior to venturing forth already felt they were risking too much and cut their losses. It just reinforced the Italian Navy not to change their plans for the remainder of the war and this is reflected in the very heavy escort duty modern battleships were doing resupply to North Africa or causing some critical food shortages on Malta by threatening convoy with 3 modern BB with a ton of support ships and various air support within their strike range.
Ironically, since you brought it up, the Luftwaffe were the only one's to actual sink the Roma, the only Italian BB completely lost during the war. And, IIRC, no Littori Italian BB actual sunk another combat ship seeing as most engagements were done at range and couldn't hit much of anything without new radar or FC system.
Strategically The Italian Navy did the best thing they could. They kept their Battleships intact, so the British were forced to keep a large naval force in the Med. This allowed the Japanese to run rampant in the pacific. A perfect example of the "Fleet in being doctrine" used to good effect. It might not be heroic but it was the right tactic.