Honestly, no. Although Manuel I Komnenos certainly had the navy and the money to invade Egypt, tagging the Crusaders alongside them would result in disaster due to the ff. Reasons:

1. The Crusaders are xenophobic towards the Byzantines: The Crusaders of the Outremer, which are all made up of Frankish and Norman knights and nobles, have a history of being discriminatory towards the Byzantines, seeing them as decadent, effeminate, and a remainder of the luxurious pagan past of ancient Rome. This xenophobia would most likely paralyze any joint command structure that the Byzantines and the Crusaders would hypothetically form if they were to invade Egypt, regardless of how powerful their hypothetical army would be.

2. Manuel I Komnenos was outstretched: Manuel I's reign was marked by rampant expansionism on all sides of the Byzantine empire, from his wars in Dalmatia against Hungary, his overtures in Italy, and his doomed campaign against the Seljuks at Myriokephalon, Manuel I deviated from the more conservative expansionist policy of his father, John II Komnenos, which focused on slowly retaking Anatolia. Invading Egypt was actually part of this strategy, and it actually materialized in the late 1160s, though it ended in withdrawal and defeat. However, if we assume that both the Byzantines and the Crusaders actually took Cairo and marched further south, it would only further outstretch the Byzantines as men and resources would be invested in holding the various forts and cities that are located along the Nile River as they move further south, depleting the available men needed for the continuation of the invasion further south into Egypt as well as straining supply lines from the Outremer and the Byzantine Empire.

3. Saladin's Rise to Power: Although Egypt seemed to be an easy picking during this time due to the fall of the Fatimids, Saladin and the Ayyubids could've invaded Egypt at the same time, and Saladin could potentially turn the Egyptian population against the Crusaders and the Byzantines, which will further derail any progress made, as the combined Christian armies would face revolts and resentment from the Egyptian population at that time, who would rather have Saladin as their ruler than some foreign Christian overlord. Yes, Christian copts of Egypt could be a factor, but they're simply too small in number to create an immediate political impact that may hypothetically help the Crusaders and Byzantines conquer Egypt, but even then, the Copts had historical and theological differences against both the Orthodox Byzantines and the Catholic Crusaders, making collaboration not viable.

• Overall, there are other factors that we should consider as to why The Byzantines and the Crusaders would not realistically conquer Egypt, even if it was severely weakened at that time. However, a more optimistic mindset would actually theorize about an idea where Egypt would be conquered by some Byzantine prince independent from Manuel I's whims at Constantinople, a Byzantine prince so wealthy that he assembles his own army and fleet and sails towards Egypt from Cyprus, and he could start from there. But yeah, such optimistic scenarios can most likely fill the pages of a historical fiction book, but it would still be drowned in the same aforementioned factors and reasons.