Well without a doubt yes, as if you really do think about it Bitcoin is able to survive and thrive (to an extent) due to the fact that the internet isn't restricted. Who knows what would happen if ISP's would force you to pay to use certain sites, such as Coinbase, Bittrex, etc.
Banks could even pay to stop users from using these sites. Who knows what would happen in the world when the internet isn't really free.
But without a doubt it would affect Bitcoin.
It won't affect Bitcoin, simple as that.
The speed needed for bitcoin txs is so low they can throttle it down to 10kbs and it's still enough. And to start filtering the traffic for BTC is going to be a pain in the ass.
Even a mining farm requires so little data transfer it's going to be easy to obfuscate
As for the third party services, who cares. Online wallets and exchanges are basically banks so using one of them it's just throwing away the control of your coins. They can't block and they won't dare to block amazon or microsoft, so I don't see the problem.