Probably not. Any hacker with two brain cells to rub together would quietly infiltrate systems in company A, from there infiltrate Company B, C & D, rinse/repeat until sufficient layers of abstraction sit between them & their target, and then use them to attack the real target. If the response of victim X is to nuke the IPs from which the attack came, they are a) hitting the wrong entity, b) potentially destroying evidence left by the real perps, and c) probably initiating a re-retaliation from the victim of their attack.
The use of jumpboxes is common when attacking targets, which is exactly what you have described. However, the idea that you just "hack back" via a DDOS isn't how it is done. Companies know that blind DDOS retaliation will only land them in hot water, so they use other methods.
A common method is a honeypot - a network segment with machines in it designed to be infected for observation purposes. Then, when activity is noticed in this network, things like trojaned PDF documents can be placed in the honey pot with titles like "All customers credit cards do not share". The attacker downloads this "great" data, opens it, and gets hacked in return.
This way, the payload is deployed against the target hosts only through the direct action of the attacker themselves.
Other methods that are similar are used, but this should give you the gist.