There are three classes of Apps.
1. Appstore Apps. These are downloaded from the Appstore and are synced with iTunes.
2. Cracked Apps. I won't mention anything more about these except to say that they also sync with iTunes, but because they don't have a valid Apple signature you can't get updated versions. It is certainly possible some future version of iTunes might detect these and do "something" resulting in anything from a stern warning, to a bill for the pirated apps, to a summons to appear in court.
3. Cydia Apps a.k.a. Jailbreak Apps. After you jailbreak the device, you can use the Cydia installer to download and install various things directly on the phone. Cydia uses a variation of the Debian apt-get packaging system, and iTunes is not involved at all. There is not a copy of the app anywhere on your actual computer, unless you work out copying it yourself using winscp or some other method.