Well, ... in a pure legal sense ... Egypt actuall was in a way allied with the CP ... as if was by legal 'arrangement' officially still subjected to the Ottoman Porte ... another sign how much "worth" international traeties actually were in these times ...
While your discussion partner IMHO grossly exaggerated the effect of Egypt participating in the Great War it would ... it could have some
interesting consequences.
As so often especially in Great Waer affairs : a lot would depend on the point of time of their joinung the CP ... or in this case rather obeying their legal sovereign : the Ottoman Chaliphate.
However, to get the ball rolling lets assume around the declaration of Jihad in late 1914 in its wake some edyptians actually start some upheaval against the british 'occupiers'.
- that would let look one strategic option for the ottomans - attacking the Suey-Channel - look much more teasing with the british forces there occupied and to a great extent unable to answer such an attack. ... aside from possible changes due to the following ...
- Gallipoli would not gonna happen at least because all the ANZACS would be sent to the Iraq, Arabia and Jemen (?) to attack the ottomans from the south and/or to the Sudan to fight/recapture Egypt ...
- which by their arrival might already be re-occupied by ottoman forces ... maybe also lead by von der Goltz (?) (him having in Egypt might also butterfly his death by Typhus away ?)
- with no Entente-forces on the Balcan - even if only on the Gallipoli-peninsula but later trabnsferred to Saloniki/continental Balcan/Greece - Bulgaria that already had a non-aggresion-pact with the OE might dicide to join the mutilation of Serbia earlier
- ... and afterwards would be powerfull enough to let Romania think, maybe rethink at least another time its points of interest (keeping at least parts of the Dobrusja and gaining additionally Moldawia). Despite the rather pityfull performance the romainan army showed IOTL in its first abiut halfyear ... it would be by A-H at least a very welcomed 'distraction' of the russians.
- the quicker fall of Serbia might have some effect on Italy as well.
- Though probably not preventing its joining the Entente it might wait a wee bit longer and set up a higher price ... like some MOARE pre-action deliveries of coal and goods of war by Britain and France.
- ... though a delay of action might already be of 'use' for the CP to get something even more decisive against Russian in 1915/16
- it also might come to the idea of 'grabbing' something in Egypt might look more attracrtive than attacking across unfavorable terrain against a now war-tested opponent on the european continent ...
- though most likely getting (once again) tied up in an assymetric (unwinnable at least in a somewhat at least middle term lasting 'rest') warfare campaign
- Not to forget Greece :
- without Entente-forces around Venizelos might find it rather difficult to set up his at least from the rightfull royal goverment in Athens almost independant pro-entente reign in northern Greece.
- with the serbs earlier (by earlier bulgarian intervention) beaten an occupation of northern Epirus of Albania - due to the unrest, almost upheaval fromany lacking executive power - might look teasing enough for Venizelos to join again with his king in a pro-CP armed neutrality
- some other 'off-spring' of a no-gallipoli timeline :
- though Enver might still slaughter his own forces in a senseless winter-campaign, most of the Gallipolo-forces of the Ottomans are available for redistgributing elsewher
- may it be in mesopotanmia throwing the indians and ANZACS back into the Shat-el-Arab, may it be in the Caucasus against the russians
These are just some ideas that came to my mind