There's a subtle difference between "not complicated" and "completely useless", thread carefully.
I'd highly suggest thinking about functionality first, and aesthetics later. It's great that you want it to alert you when it moves, but how on earth is that a good alarm system? You do realize it would probably start ringing if the car was parked and there is a bit of heavy wind? Not to mention the fact that it would alert you every time the rightful owners uses the car, since an accelerometer hasn't got the brains to figure out who's driving. The amount of false-positives you'd get are rediculous.
Then there's the whole power issue; plugging it into the cigarette lighter would waste that port for useful purposes. If someone was like:"I need to charge my phone/navigation, let's switch it out", the alarm would trip (again, those darned false-positives). When/if you unplug it, it'll need power to send it's alert message, for which a coin cell probably won't suffice, considering that a cellular chip needs quite a bit of power. Not even if you use it "just as backup". It's like trying to jumpstart your car using four triple-A batteries, admirable, but not really functional.
And like @smogs mentioned, it'd only have power when the keys are in.
So, about the 'stickable' thing... Why would you want it to be stickable? I get that your like to retrofit it into existing cars, but are you planning on moving the device very often, or is it a one-time stick?
Functionality issues: imagine you 'stuck' your alarm on the inside somewhere, a thief broke in and is highly unimpressed. He sees the thing and unplugs it, then he drives off with your car.
Problem 1: the alarm should've gone off before he unplugged it, otherwise it wouldn't do anything if he didn't unplug it, which is rather useless.
Problem 2: he drove of with your car. Let's imagine you were out of hearing range and didn't hear the 'normal' sound alarm. So, now you've got a mobile notification that your car has been stolen. Then what? It's not going to help you get it back. If just let's you know what you would've figured out had you gone to the parking lot later.
Are you aware that neopixels can use up to 60mA each? Your battery won't like that.
"If the car senses a possible steal", how on earth does it do that? As human beings we're quite adept to figuring things out, but even I have a difficult time figuring out what other humans are up to. I'd be amazed if you could point me to a sensor that could identify potential thieves, as I'm sure the cops would as well.
Accelerometers are good for one thing: detecting acceleration. Unless proper additional logic is applied, an accelerometer won't detect the difference between you driving your own car, or someone else stealing it. That kinda defeats the purpose, doesn't it?
So the things you need to figure out before planning on where to place it:
-How can I accurately detect possibly theft, without alerting me when the car is in normal use?
-What do I want to achieve by having this system? Notifications only, or something actually useful like being able to track it when nessecary?
-How do I power it, properly?