Supplies flowing from Italy to Libya in 1940 were abundant. The Italian navy did an excellent job, which is why the British captured 130,000 prisoners and enough cannon, machine guns, ammunitions, etc, to supply Greece (ironically Greece defeated Italy with guns captured in Libya), not to mention the large number of tanks and biplanes destroyed by the British. The Italians had few planes and no artillery that could stop the British Matilda Tanks (which Rommel destroyed in Arras with the 88 mm Flak), so sending German planes, tanks and leaders to Libya changes completely the picture.
Even in 1941 the Italians did an excellent job supplying Rommel with hundreds of thousands of tons. However, the problem was that Germany was fighting in Greece first and after June 22, 1941 did not have access to Soviet oil on credit and had few guns to send to Rommel, because they were sent to the eastern front.
In the summer of 1940 with Soviet oil, an almost intact Italian navy, axis control of Malta and with Germany and Italy not fighting anywhere else, capturing poorly defended Egypt (which cannot be supplied except sailing around Africa) is a given.
By the way capturing Malta in July 1940 not only ensures safe passage for the supplies to Libya and prevents the British from supplying Egypt, it also prevents the British from sinking the Italian Battleships in Taranto much later in the year. So these ships can team up with the German planes to expel the British from the Mediterranean, the Red Sea and a good part of the Indian Ocean. Once Britain is out of the war they can sail to the Black Sea to help the invasion.
Given the series of debacles that the UK had suffered throughout the war, I venture to say that as soon as Alexandria falls to the Axis, Churchill will have to sue for peace.
1) That the Italians transported a lot of supplies to Tripoli,is irrelevant,because,once the supplies were in Tripoli,the ptoblems began :it was very difficult to get these supplies from Libya to Egypt,thus,the fall of Malta would change essentially nothing .
2)There was no way the Italian navy could go to the Black Sea:there was no oil
3)the capture of Egypt(1940 or later) was impossible,because it was impossible to supply a motorized army from Tripoli(it was possible,from Alexandria,but,with very big difficulties):it took Montgomery 3 months to go from Alamein to Tripoli.The war in NA was determined and limited by logistics(see :Logistics and the Desert Fox)
4)As the Mediterranean and the ME had only a minor importance(Britain could do without them),Churchill would not ask for peace .The importance of the Mediterranean started only after the war .
Before the war,Britain imported yearly some 12 million of tons of oil and these were coming from....
1)the Carribean :46.2 % =5.54 million
2) Iran and Iraq :30.8 %= 3.7 million
3) the US :19.2 % = 2.3 million
4) the rest came from Rumania
The following are the production figures for 1940
The Carribean:30.7 million 10.5 % of the world total
Iran and Iraq: 11.3 million 3.8 % of the world total
the SU :30.5 million 10.5 % of the world total
The USA : 182.9 million 62 % of the world total
Total : 293 million
Due to the Italian DOW (june 1940),Britain decided to stop the import of oil from the ME :the Mediterranean was to dangerous and the route via South Africa to long,thus,the SMALL amount of ME oil 3.7 million was easily replaced by oil from the US ;it was no problem for the US:3.7 million was only 2% of their production .
Btw :I should not exagerate the importance of the oil that Germany got from the SU,this was only a small part of the German consumption ;the most important were Rumania and the home production .(this,during the war,before the war,it was,as for Britain,the Carribean)