If you were to have your own DoS (Denial of Service) attack then it could choke your own internet at the same time, depending on your internet bandwidth and whether you could saturate it on your upload.
A DDoS (
Distributed Denial of Service) comes from multiple machines spread over many different networkss, so in this instance its less likely that those participating in the DDoS (or those that are unknowingly part of it through malware) would have their own internet connection saturated.
And I misinterpreted the question...
No, the whole point of a DDoS is that your hitting the website/network with so many requests for information that either their internet connection becomes saturated or their hardware cant keep up, and hence becomes unusable to anyone with genuine business there (thats why its called Denial of Service).It doesn't even necessarily require specialized equipment/software either, if you had enough people, going to a website and having everyone spam F5 would be a DDoS attack. The people doing the attack themselves wouldn't have access to the website during a successful attack. Typically when websites are defaced during DDoS attacks its through some other means of accessing their network, as on its own a DDoS has no ability to damage or change the website.
Despite what movies and what hackers would want you to think, a DDoS is the equivalent of hitting a website/server with a hammer until it stops working.