Nah, the invasion wasn't necessary in the slightest. With the opportunity costs involved, the operation is likely a net negative for the Initiative as a whole. And definitely a net negative for humanity.
Even if Kane never pulled his deus ex machina and never offered the TCN, the resources and lives expensed here would have been better used on evacuating people to space or combatting Tiberium.
That said, while the operation may have been a net negative, it wasn't wholly useless. It strengthened Seo's political position, temporarily satiated the Initiative First and other elements hungry for war, expanded the amount of dirt the Initiative controlled, expended a large portion of Nod's nuclear arsenal, cripples a Nod warlord, captured millions of Nod civilians, and strengthened the Initiative's logistic chain.
How much of a net negative it has been is not yet decided, bear in mind its not over yet. There is still Phase 4 and 5 of Karachi to complete, and that likely incorporates a strengthening and expanding of the BZ18 linkage, along with more operations against the Shah of Atom.
The long term balance of power is being shifted, how much is lost on the GDI's end from nuke strikes and damage to our ever stretched navy remains to be seen.
As for NOD, well, the canned sunshine has been opened and there isn't really another way for them to hold the GDI back. The next logical targets of Mondragon and Reynaldo are likely the ones most desperately trying to acquire strategic deterrents. The latter likely already has them (though given the leash Big Daddy Kane put on Reynaldo during the regency war him using them is an open question), the former is probably gonna try to team up with Stahl but the logistics links between them are tenuous even for NOD. Krukov will likely absorb what remains of Al-Isfahani's organization if there is any remaining post Karachi.
The real question is, do the Bannerjees try to strike Karachi and the BZ18 linkage before we secure it or not. This would be the right move militarily for preventing our objectives, but it would break the Pacific Conference Treaty and potentially kick off a second Regency War, this time with us pulling Operation Eastern Paris. The Bannerjees escaped any major fighting last time, they would not this time.
So think we are gonna have to spend a lot of dice on getting Karachi up and running very fast along with more of the defence options
Current progress remaining for Karachi is: 178/390 (Phase 4), 0/780 (Phase 5) total of 178/1170 Progress.
This should cost us ~11 dice on average (assuming 5 Infrastructure and 6 Tiberium). Possible to do in 1 turn, but we will need likely need 2 as a bunch of our dice need to go to repairs (for Infrastructure) and fighting the Tib (for Tiberium). This will narratively also give some time for our supplylines to become more well established. One of the big things emphasize in the recent post was the strain this operation is putting on our logistics, so taking it a bit slower with ~2 Infra and ~3 Tib dice this turn is not nessessarily a bad thing. It will be better in the long run, but in the short term we are burning through stocks.