The Ad Hoc idea won't work, but not because of the iTach, it's your iPad. The iPad must connect with a network and get an IP address, whereas the iTach has a default address that you could change manually, or make static. It's half of an Ad Hoc network, but the iPad won't co-operate to act as the other half. So, you need both on a WiFi network. It could be the same as your home network, that's not a problem.
iTach doesn't need an internet connection to work, but your iPad will be much happier if it's on one. You'd be able to use apps like IMDB, for example, along side your control system. Nobody can access your iTach from outside your network unless you set your router up to permit it, and by default a router won't allow it.
Your home network is fine for the purpose, and your existing router will handle the addressing just fine, but both the iPad and iTach need a good WIFI signal, so you'll have to provide that first before you can go much farther. That's done with an access point (basically a wifi only device that uses your router to handle creating a network), and there are many options for that. A relatively simple low cost access point would be the best choice. You'd want it wired to your home network for best performance, though some can extend an existing wifi net without hard wiring. Once you have both the iTach and iPad in a good wifi signal area, all the rest of this will be much easier.
A stand-alone wireless router might also work, some will let you set up a local wifi net without a WAN, but others will gripe about not having a WAN connection. It's not a great idea because your iPad won't have the benefit of an internet connection. I suggest the access point solution, and either wire it to your existing network, or get one that will extend the existing wifi.
However, one caution based on your question. You may not have a lot of networking experience, and if that's true, you may be frustrated with some of the setup. Global Cache devices are very cool, but can be a bit ornery at first. Knowing how to access your router and its device list is very helpful, and understanding some basics re: ip addresses is essential. In general, network based control with these devices is either a rather deep "hobbyist" project requiring a lot of time and patience, or something better handled by a custom integrator. It's one of those unfortunate areas where those that already have the understanding don't need any instruction, and therefore there isn't much around to help the novice.