The Fourth Crusade is not a good comparison to determine how Crusaders would treat the Copts. Several important elements are unique to the sack of Constantinople.
1) Over a century of stories of how perfidious Greeks betrayed or undermined the Crusader efforts.
2) The huge debts wrung up by the Fourth Crusaders that needed payment.
3) The feelings by the Fourth Crusaders that they had been personally betrayed by not being paid for their efforts to restore Isaac II and Alexios IV to the throne.
4) The extremely bad strategic situation of the Crusaders that gave them the options of being eventually massacred, or seizing absolute power for themselves.
This explains the pillaging and conquest, not simply because they were Orthodox.
In the actual Crusader states, the Crusaders were actually fairly tolerant of the various religions living there because they knew they relied on them for taxes, supplies, and survival. This included Orthodox and Syriac Christians. The Copts would be treated the same way.
Of course, the major problem with the Copts is that as monophysites, they can't be in communion with Rome since they deny Chalcedon. There will eventually be tension there, as at some point Rome will attempt to bring the Coptic Church into orthodoxy. I think it will be some time before they do that though. So while the Coptic Church won't flourish, it won't necessarily be any worse than under the Muslims for some time. If the Crusades will rule Egypt permanently, we may not see any real trouble for 1-2 centuries. The Crusaders will be too busy simply keeping Egypt at peace to be bothered with forcing the Copts to convert.