Synchronicity is a new tweak available via Cydia Store which lets you use your iDevice while it Syncs with iTunes! Can you Handy?  Synchronicity costs only $2.00 and works on all iDevices we have tested it on the iPhone 4 & it worked like charm. To Download Synchronicity simply launch cydia and look for it under Cydia Store.

Requires iOS v4.0 or higher.
Use your device while it syncs with iTunes!
Synchronicity gives you the option to use your device during an iTunes sync. Instead of being stuck at the lock screen while you transfer new content, you can unlock, run apps, make calls, etc. You can do whatever you want, except run the Music app, which is disabled during syncs to prevent data corruption.

Synchronicity works on any device with firmware 4.0 or 4.0.1.

Though overall performance is virtually unaffected, you may notice slight lag in certain resource/CPU-intensive operations.