The short answer is Yes. An inventor is granted a one year grace period where their disclosure is not considered prior art for their invention. However, posting an App without first obtaining any patent protection is a risky proposition. Previously, the law followed a first to invent system. This means that if an inventor could prove (1) their invention was conceived before the effective date of a relevant prior art reference and (2) due diligence in developing their idea in a reasonably timely fashion, the inventor may still obtain patent rights for their invention by disqualifying the prior art by the showing of earlier idea conception.
Recently, there was a change in the patent law and the AIA was implemented. Under these new laws, the first to invent system was replaced with a first to file system. Therefore, even if an inventor could prove his invention was conceived before another disclosure that qualifies as prior art, such proof would be irrelevant.
Therefore, if you post an App in the App store without protection, a 3rd party can copy your idea without suffering any penalty. Additionally, the 3rd party can modify your App by making certain changes or improvements and file for a patent on the App that you conceived. If that 3rd party files a patent application before you are able to file an application, that could spell trouble for your application because the application of the 3rd party may count as prior art against your application. In other words, the Patent Office may reject your application because a 3rd party copied your invention, modified it and submitted it to the Patent Office before you did.
The best way to safeguard your App is to file a patent application as early as possible. A successful patent application helps to protect against any inventors that follow subsequently with a similar or identical idea as well as potential infringers. Any idea that can be successfully commercialized has value and obtaining patent protection is one of the main vehicles used to prevent any other person from using your idea. In the event that budgetary costs are of your primary concern when applying for a patent, then filing a provisional patent application is a great way to protect your idea while securing an additional year (from filing the provisional patent application) to generate funds to file a utility patent application.
If you have a question regarding patents or intellectual property, feel free to contact me.