No. Either way you're going to have to launch an app in iOS to share a message to Facebook. You can tweet pictures straight from the photo gallery, but if you want to post to Facebook then you have to launch the Facebook app and upload the picture from there. Instagram doesn't really solve any issues because now you're just launching another application instead of Facebook.

I thought the initial problem Instagram solved (before its own network became popular) was that you could launch one application are share multiple places (and I suppose eliminating another app from the flow with filters).

However, since I'm an Android user I could easily mistaken about this.