The wireless Genie client can be used with either the HR34 or HR44 Genie DVRs, and can be used in combination with other C31 and C41 clients. You can use the Genie DVR and up to 3 clients (wired or wireless) at any time. The wireless client does not depend on your wireless network at all. Instead it uses the DIRECTV Wireless Video Bridge to create a secure wireless network that only communicates with your clients. That means that you don't even need wireless networking and your DIRECTV experience won't be impacted by any other network traffic. The Wireless Video Bridge needs a coax connection but it has a passthrough feature so it can share a line with the Genie DVR if necessary.
Here's a diagram of how the system works:
The wireless video bridge connects to the splitter. It can be its own coax run from the splitter or, as shown, you can pass the satellite line through it to your Genie DVR. Regular Genie Mini Clients connect as they always have, but the wireless client doesn't need a coax connection at all.
All three clients can be wireless if you would prefer and all of them can share the same wireless video bridge.