No. Not one single bit. A content provider pays for their pipe to the internet, and that space of the internet's service providers is bountiful with competition.

Say you are Vimeo, which is sort of Youtube's tiny little cousin. You rent your super huge (fast) pipe to the internet. It costs you (made up number) $100k/month. You shopped for that pipe, you have a 20 page contract with an aggressive SLA (service level agreement), oh, and you probably also have a secondary pipe, atough smaller, with a totally different provider - again with a big-ass contract with a set in stone SLA.

Now if they say "hey, you didn't pay us enough, we're going to throttle you", oops! You have a contract, a powerful contract - and most importantly, you'll just jump ship and start doing business with another provider.

Even if Vimeo only has one telecom company providing the fiber to his data center, that's ok! In the US business pipes like this must be "rentable" by 3rd parties. As in Joe's Internet Access Company can (and does) rent the fiber connection (or space on one) from - say - AT&T - then passes that part of the bill along to the customer. The BIG cost is connecting to the internet, via a backbone provider. And backbone providers do not throttle, nor will they, again, too many players to connect to.

Now our issues at home is we only have 1, or 2, in a very tiny few cases 3 providers from which we can choose. Over 50% only have one choice, and two choices is a duopoly - and a duopoly is generally as bad as a monopoly. Which means if net neutrality dies, they can play games with our pipes. Either charging US more for decent transit, or (more likely) charging the bigger players big money to transport their bits to us unfettered.

TL;DR - nope, you're golden!