No, but by that logic such connections existed less before Facebook etc. And this is indeed probably true. And I say that as somebody who doesn’t use Facebook any more, and who lives abroad.
What does "connection" mean to you in this instance? That's the sticking point here. If a "connection" is simply "I can see a post written by that person every now and then" well, I'm gonna go ahead and say ridding yourself of that won't actually harm you socially. I absolutely question self-defined "relationships" that are held together by mass broadcasts of carefully crafted messages. For me, that's not a relationship. Granted, that's not a decision for me to make, but regardless. I fear we've all redefined what a "relationship" is without actually considering the ramifications.
By connection I mean any relevant/enriching piece of communication. Furthermore, apologies for being a bit flippant but if the only things you see on your Facebook friend feed are empty fluff then maybe you need to find more interesting friends. The medium itself may not be particularly enlightening but it doesn’t fundamentally prevent meaningful interactions.