It depends on what you commit to Egypt and what Italy buys.
If you bring stuff from India, then yes Egypt will hold.
If you bring all UK air, then yes Egypt will hold.
If Germany stations some air in Alexandria with the Italian stack, it may be able to do some damage on ships in the Red sea. Or, depending on the size of the British fleet at Gibraltar, German subs/air can take it out, even with 3 fighters scrambling.
If Italy keeps its fleet from turn 1 (only the ships at Malta die), they can block the SZ 92 fleet from interfering for one turn and land 4 support land units in Alexandria (or Syria if they don’t have the odds on Egypt turn 3) with its North Africa troops. German air land there turn 3. From there it depends on what you committed to Egypt. Even if Italy cannot take it, they can tie down lots of UK assets there that would otherwise help in other areas.
If you dropped units in Syria, they can get the free Iraq units and be a pain in the Mid East.
My whole point of this is the attack on the Italian fleet is totally worth losing the starting British fleet in the Med, for Italy never recovers if you keep the heat on.