Yes that would work, but you will find that it probably is a smoother operation going thru the NVR.
You will find that putting cameras on your router will open you up to being hacked. And they are not hacking to see your video feed - they could care less about that. They use your internet for DDoS attacks and to get into your system to steal your bank account info. We have a couple of threads just this week where people are seeing connections or attempted connections due to this.
Further, you will start to notice things slowing down. Cameras connected to Wifi routers (whether wifi cameras or hard-wired) are problematic for surveillance cameras because they are always streaming and passing data. And the data demands go up with motion and then you lose signal. A lost packet and it has to resend. It can bring the whole network down if trying to send cameras through a wifi router. At the very least it can slow down your entire system.
Unlike Netflix and other streaming services that buffer a movie, these cameras do not buffer up part of the video, so drop outs are frequent, especially once you start adding distance. You would be amazed how much streaming services buffer - don't believe me, start watching something and unplug your router and watch how much longer you can watch NetFlix before it freezes - mine goes 45 seconds. Now do the same with a camera connected to a router and it is fairly instantaneous (within the latency of the stream itself)...
The same issue applies even with the hard-wired cameras trying to send all this non-buffer video stream through a router. Most consumer grade wifi routers are not designed to pass the constant video stream data of cameras, and since they do not buffer, you get these issues. The consumer routers are just not designed for this kind of traffic, even a GB speed router.
So the more cameras you add, the bigger the potential for issues.
We strongly suggest you do not run the cameras thru the routers....