I was wondering if it was possible to sync hacked apps to a restored, unhacked iPhone 3G...

The process would be:
- Hack iPhone
- Install desired apps
- Sync the hacked apps to iTunes on computer (is this even possible? I have a Mac [PowerBook G4])

THEN:

- Restore iPhone 3G to factory settings (and remains unhacked)
- Sync hacked apps to newly restored unhacked iPhone 3G (is the transfer possible?)

I would have tried this on my own, but I have a feeling someone has already done it. However, I haven't found any related postings. Anyways, I wanted to know if this process is possible with all the app transferring, and if so, would these apps function properly on an unhacked iPhone 3G.

If the hacked apps were able to be transferred to the restored and unhacked iPhone but somehow these apps were recognized as not purchased, would there be a purchasing charge applied or would they go unnoticed?

Thanks,
Jayson P