...but it does leave the open question (that I'm sure a good answer exists for) of how the AP manages the DHCP router <-> AP <-> Wireless Client connections.
Your question crosses OSI layers, so it's unanswerable. The AP doesn't know or care what DHCP is, or what IP addresses are. They have no relationship whatsoever.
Skip this if you already know what an AP is, and how that relates to the OSI model:
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An AP (and I don't mean a router that has an AP in it; I mean the singular entity) doesn't operate at the network layer. It operates on the physical layer, in that it converts between "wired" and "wireless" traffic. There's also another entity that is usually (incorrectly) grouped in with the AP that converts between 802.1 and 802.11 (data-link layer) traffic. The reason that this is incorrect is that there's no reason you can't have 802.11 data on a wired network. This work is done on the CPU of the router in the case of the 300N, but it's important not to confuse the idea that they are separate entities.
An example of wired 802.11 traffic is those wireless things you could buy for the original XBox - when the box detected one connected, it would speak 802.11 instead of 802.1 over the wire, and then all the wireless dongle had to do was blast the signal over the radio. If those things could auto-negotiate channels (some of them could, but the cheaper ones required manually selecting the channel), they'd have been full-fledged APs.
Even if you use AP to mean both of these entities (and I will do so, going forward in this post), there's still no bearing on DHCP or IP - those are network layer protocols, and reside inside of the 802 (data-link) tunnel. The AP considers that stuff to be payload, and will never attempt to read in to what those packets mean.
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An AP is the wireless equivalent of a switch. It knows about the data-link layer because it has to send the frames to the right physical location (in 802.11N, the 3 antennas are used to "direct" the wireless traffic), just as a switch uses MAC addresses and a routing table to send frames to the right physical port. This is why a MAC address is called a
physical address.
By disabling DHCP on the router, and not using the WAN port, the router is effectively disabled, reducing it to a switch and AP. Placing a crossover between the 300N's switch and the other box's switch creates a larger switch, and makes the AP accessible to the entire LAN, including the router with the enabled DHCP server that's performing NAT. The wireless clients will be bridged in to the same LAN as the wired clients.
Well, so an interesting question here: should I connect my switch to my wired router with multiple connections? Will there be a bottleneck between 8-12 DHCP clients being served through one wire?
Yes, there will be a 100MBit or 1GBit bottleneck, depending on the speed of the slowest port the crossover is connected to. Using multiple links won't help; the switch will pick whichever one it thinks is faster, but will not use both at the same time.
