There's two models of the cheetah - both have a shock sensor, a current sensor to detect ignition on/hotwire, and an accessory wire. The expensive one also has an "intelligent" tilt switch as well (it's a separate plug in module). The idea is if you leave a bike on either the side or centre stand the "intelligent" switch will detect a change in it's position if moved. However you then need to find a place to mount an extra module about the size of a pack of cigarettes, and our bikes don't have centre stands so don't need the "intelligent" switch. There's a low-tech solution - I used the extra "accessory" wire with a cheap ($2) mercury tilt switch.
The accessory wire's there for things like hard bags or fairing compartments etc that you want the alarm to protect by installing extra switches. Just wire one side of the mercury switch to the wire, and connect the other side to the bike's frame/battery negative then use some double-sided tape to stick the switch under the frame's spine. You'll want to play with the exact position of the switch so you can stand the bike halfway upright before it goes off, or you'll have problems when you park on a hill. There's instructions & pics for this on my site.
The shock sensor's adjustable (and can be disabled with the remote) but even at it's most sensitive you can get around it by moving the bike carefully. It's really only to protect against someone vandalising your bike. So yes without some sort of tilt a very careful thief could potentially wheel your bike away. Putting a disk lock on too will of course make it that much harder, but they're a pain if you're on and off the bike a lot.
Given long enough anything (even humidity) will drain the battery. However if it's in good condition and fully charged you should be able to get away with a week. (Having said that my 3 year old battery will only last 3-4 days without a run.) If you're worried about it just don't fit the LED - chop it off and tape up the end of the wires. You could even put a small switch in one of the LED wires to give you a choice. Something to think about is that if you're only riding once a week or less you should install a power socket on the bike (triumph have an expensive one, but it's a standard bmw part and you can pick them up all over for much cheaper) and use it with a battery tender to keep it topped up.