I was just looking through my stats and this question came up in my server logs. My first thought was if you spent the time to think about it and type that long-assed question in my search box then you probably already know the answer.
YES it will. Buying traffic on Fiverr may be a good short term strategy but Google will eventually see what you are doing and your site will be penalized and found at the bottom of the search results. While Fiverr is a good place for some things I wouldn't be caught dead buying traffic or buying backlinks or link wheels or anything like that.
I use Fiverr to get logos, and maybe get some videos made. You would have to be crazy to use a site like Fiverr to have anything done off page for a website that you care about. Think about it for a second. Say you buy 50 backlinks, all of them are on garbage sites and 50 other sites have the same backlinks as you. Sometimes they are the only backlinks a site has. How easy is it for Google to go in and see these backlinks and realize that they were bought links. It is simple!
Odds are I would be able to see that you bought links or even worse link wheels from Fiverr and I don't have the expansive knowledge that Google has in its arsenal. Unless you don't care about the site you are building and only want a 3 week boost for your site then you can buy traffic from places like Fiverr. I have nothing against them but using it to get traffic to your site is not sensible.