It really depends what do you mean by "survive". BTC might still exist but it might as well be irrelevant to the general populace as something new and big might come by to replace it.
If by "survive" you mean BTC being the #1 crypto in terms of price and market cap? That might be it as well.
But we've seen BTC already being challenged by ETH at this very moment with ETH passing it in both transactions and nodes.
No, and I would be disappointed if it did, thats stagnant AF. As much as I like bitcoin, there is no way it will still be here 100 years later. at least, not like this; it would be a legacy system people only used out of nostalgia. We already have better implementations of crypto in my opinion, but they simply arent as trusted as bitcoin is. primacy means something here. look at how much progress we have made with blockchains in general. It will take a generation that grows up with the blockchain concept to foster its evolution. after that, bitcoin wont even be the coolest kid on the block anymore.
Think of it like cars. While we still have cars, many years later after their invention, no one is driving around in a Model T anymore.
Bitcoin is that Model T. 
It wont be eth either. sorry fanbois...
Haha, don't be so absolute now, the thread is about speculations. Until these 100 years come we cant know what will happen to bitcoin