Except for that, I’d say “rock on”. I’ve set up several customers with a setup just like you are describing without the dedicated box. You can even install/enable the DHCP server on FreePBX to only provide services in the “dedicated” network and let another DHCP server handle the other network.
There are so many ways to do this; most of which will work.
One NIC - assign addresses to everything and connect everything to the same network switch. This can get complicated, but once set up should provide a reasonably solid experience.
Two NICs - put the phone network on one NIC and the rest of your services (and the VOIP box) on the other. Set up a “static route” to the VOIP box so that your VOIP traffic gets routed out correctly. You may need to set up a second address on your “network” NIC to talk to the VOIP interface. Your installation engineer should be able to help you with that.
Three NICs - put the VOIP box on one, VOIP network on the second, and everything else (including the “default route”) on the third. The advantage here is that the network paths are clearly delineated and each port has it’s own specific configuration.
QoS is a routing protocol issue. If you have a separate physical network for your phones, you do not need to be concerned with QoS on that network - all of your phone assets will benefit/suffer from being on that network together with no real differentiation. The place where QoS will become important is in your mixed-mode network and in your external connection. Since you are using a dedicated VOIP interface, one could reasonably assume that, like the physical network, there’s no QoS risk/reward since the network is once again dedicated to voice traffic.
You can assign more than one IP address to a NIC. If you do this (or go with some even more exotic, like VLANs), you can have all of your traffic running on your basic network infrastructure, but it’s no longer dedicated. At this point, you run into spots where you may need to be able to tune your network to get the kind of support you need for voice.
If you have the resources, I’d recommend against this “shortcut”. Having a dedicated network for your phones and another dedicated network for the rest of your equipment is a solid approach and, with the prices of switches these days, a solid way to provide reasonable levels of support to your customer.
So, while there are lots of things that may need to be considered in the long-term, in the short term you can get started with whatever configuration you feel like working with. One, two, or three Network Interface Cards can be used to make this configuration work; analysis paralysis can set in if you try to solve a problem with too many variables.