As
@MattW said...not necessarily. The issue a lot of our clients have run into using a CDN (especially CloudFlare) is that it's often times quicker to go to the server itself, instead of through the CDN's server, so some people will actually see a performance DECREASE. Where you are generally likely to see the benefits of the CDN is in other countries.
It is unlikely that DNS is where the delays are occurring. That's SO rare, but it certainly can happen, especially with somebody like GoDaddy, where their DNS servers are very likely overloaded.