Can text messages sent via Global.AQ Lite (iPhone App) be traced?
The answer is yes and no. She can not find you. The police ultimatively can track you down but its taking a lot of time and effort which might not be worth doing so. 

The procedure would be:
a) The police opens up a criminal case
b) the police identifies the sending number
c) the police identifies the sending SMSC
d) the police ask the prosecution of the country of the sending SMSC who the sender was. This will most probably track back to a SMS aggregator. Going up the chain they will end up on Global.AQ provider.

e) The police of Switzerland would have to hand over a court order to the Global.AQ provider (Fink Consulting GmbH in Switzerland) to hand over the identity data of the person who sent the message. A court order is required by law. The laws of data protection and the laws of telecommunications in Switzerland prohibit to give out any information about any telecommunications occuring or their contents to anybody. This is the case in most countries but some countries, such as the US give that information to the FBI or CIA without a blink of an eye. This is not the case in switzerland however where the rule of law is followed strictly in those matters.  Any information of the content of the communication is only available to the police in case of serious crimes. The information on who is the owner of the number is however not restricted to the serious crimes.

f) The identity data would include your e-mail address used at signup, your name etc. which you used to sign up and the IP address. All of which could be hidden/faked to some extent.

g) the IP address then can be tracked down to the mobile phone operator or Wifi access point from where the message was sent.

h) the police now could know you and could prove you sent the message and could go after you.

All this would probably not happen if you are just a bit rude to a person. If you threaten to kill someone however such things can happen quite fast as life is considered in danger. It's also a question on if the police does want to do the effort of all this for a simple case of one time stalking.

So far the above procedure has happened only once in the lifetime of Global.AQ where someone was making a joke of placing a bomb. The receiver however has not considered this as being a joke but has taken it for granted and launched a chain reaction in police work.

My recommendation: be polite to people avoids the problem in the first place. It doesn't help to piss people off. It might fire back on you some day. Maybe in 20 years when you apply for your dream job but the HR manager of that company is the person you insulted and the person remembers it. In other words it never pays off to be evil.

Hope this answers your question

Andreas Fink
Developer of Global.AQ