You have 2 architectural problems
1. As you identified, the MD access would be through the "external" interface of the LMCE core server - you will not be able to get this going without a huge fight. That architecture is not supported, it will disable a number of the features and likely be unstable - do some searches on the forums for singe/1 NIC to see the previous discussions/flame wars!
2. As bumaster108 points out... to clarify, you will not be able to boot MDs wirelessly with just a wireless card - this is because the MD system boots using PXE from the BIOS. Even if you purchased a second wifi access point for the internal network to resolve point 1, when the BIOS starts PXE you will have no ability to configure the wireless card to associate with your internal WLAN, set the encryption levels or keys, etc.
As mentioned, to resolve point one you need a dual NIC (standard architecture) core, with a wireless AP on the internal network. To resolve point 2, you could either setup a pre-configured wireless bridge plugged into each MD's ethernet interface. Or possibly using boot to USB thumb drive with a GRUB loader on it which you could then string together some utilities that would allow you to load drivers for the wireless card, set it to associate, then manually kick off the boot process - but this would probably only work after you have initially built the MD image. Either way, I wouldn't recommend it as it will be a lot of work to set up, and streaming video over wireless can be very subject to interference from microwave ovens and cordless phones, etc...
It is a pain, but you would be far better off to run cables and hide them under carpets/rugs, nail them to skirting boards etc!