As with anything, if you put enough money into it, it could be done. But, in this case the time/effort/cost far out weighs the end result.
In short fr 4WD, your looking at welding in a new floor with fabricated tunnel, more than likely custom running gear inc drivesahfts, moving the fuel tank, probably re routing the exhaust and new gearbox? Or somehow getting the drive to the rear wheels from the standard gearbox. And more than likely a million other things too.
Not much change from 9-10k i wouldn't have thought. And you'll probably find it hard to get anyone to give you an accurate quote before the jobs done. Sell up and buy an S3 or Golf 4motion etc if 4WD VAG is what your after. If however your dead set on a 4WD
Ibiza then be prepared to spend thousands and never ever make any of it back when selling.