Depending on what you do, Italy could attack you in Egypt and take it or cry and beg.
In Africa, Italy has: 6 inf, 2 mech, 1 art, 1 tank. And 3 inf in Ethiopia and Somalia.
Uk has 3 inf, 2 art, 1 tank, 1 fighter, and 1 inf in Sudan. And 1 ANZAC inf!
If you build no IC and wait for the Italians to come, turtling in Egypt proper, their african forces may break you (10@1 2@2 1@3 and probably their fighters, against 7@2 1@3 1@4). If they do not, there is no problem, because they could ship troops in your face while bombing you from the sea too. The british african army is dead if left alone.
But they can buy time. You can give them Alexandria while trying to kill the Ethipian forces with your transport. You can especially try to destroy part of their fleet and one of their transport. Even if you lose your own mediterranean fleet and your egyptian fighter doing it, Italy will be crippled. You’ll win at least 2 turns as they’ll need more time to prepare. And as you can buy time, you should buy an IC in Egypt too, so you could defend it and make sure the Italians never become anything close too an important power in that game.
The Global game will be much more than one Pacific and one Europe game side by side. Japan must not attack J1 if it wants its allies to live. UK then has a chance to make money in Pacific for at least 1 turn, and this means that an India crush strategy will probably not work. At least not by turn 3. This also means that you could maybe spare 1 or 2 planes from India to Egypt, where they would completely change the balance of power.
I would then do not even consider constructing an IC in West India. Ab IC in Egypt and some troops shifting between Suez and Calcutta should do just fine.