Is it possible to track what personal information an app is unloading? In general, the answer is no.
Sniffing the precise data the the software is uploading - either through installing some specific software on a rooted device, or by sniffing the traffic elsewhere between the device and the Internet (e.g. on your wireless router) - is a very good idea and will help you understand what the application is doing, but unfortunately the actual information might be mangled in some form or even encrypted, in a way which will prevent you from really knowing what the application is sending.
Actually, it's a known security problem - for instance take a look at this academic paper, which proposes a way to track how your personal data is used during the application execution; though its proposed approach does have some limitations and can be circumvented by other tricks.
My personal rule of thumb is to avoid applications which require both Internet access and access to private data, unless I have a high level of trust in the author.