R7800 as extender?

No. 

Ap mode it needs to be hardwired in. 

Bridge mode doesn't rebroadcast. Its designed to use the wireless as a "bridge" from router to router with the 2nd one being able to use its ethernet ports but not rebroadcast its wifi. 

You could always use it in ap mode and connect it using powerline or moca adapters if you didn't have an ethernet connection

There is some aftermarket firmware for the R7800 if you do a little googling that might have that capability. 

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perseid wrote:

Yes I read that Extender mode is not supported in the R7800. Will AP or Bridge mode work the way I described?

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Hard to know what you mean by "as described".

You said earlier:

The idea is to have the R7800 in wireless mode (not cabled to the RAXE500)

The R7800 clearly won't work in AP mode like that. AP mode = wired to the router.

The manual explains how to set up the R7800 in "bridge" mode.

Visit the support pages:

Support | NETGEAR

Feed in your model number and check the documentation for your hardware.

Check the section in the manual Use the Router in Bridge Mode

You also said:

 

to maintain the same SSID so that devices that connect wirelessly do so in smart roaming mode

 

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That might not be the best idea. With the same SSID and password, wifi clients could get confused.They will have to negotiate a switch between to wifi sources no matter what the SSID and password.

Genuine "smart roaming" requires cooperation between the main router and other wifi sources. That is what Mesh is designed to do.

By all means try your approach, but check to see that it is any better than having separate identities on the wifi sources.