No.
There never was an installer that could be used on mid-2011 iMacs later to install Mac OS that shipped from Apple on DVD. The recovery require a working an ethernet connection or a good strong secure WiFi, if you can ensure you are entering the WiFi password in the right place.
The High Sierra installer on eBay hopefully is just a raw installation created with a package software that creates your own discs and flash media and doesn't include any of their own custom instaled software on the installer, and hopefully they kept it in good shape. Generally I keep clones of my olde tr operating systems to restore from external hard drives. That's the only way I can guarantee that I have an older system available to me.
You may want to bring the iMac and its power cord to an authorized service centre and see if you can run recovery there. http://www.apple.com/buy
If it works there, and not from home, someone needs to reconfigure your router so it doesn't block Apple's installers.