Anything is possible with enough $$$$$$$$$$... and this conversion would not be cheap.
You would need a complete motor w/all the sensors, ECU, wiring harness spliced in to work with the MKIII interior (tach.. etc). Custom motor mounts to fit the MKIII, an R154 tranny (used in all 7MGTE MKIII's) with either a custom bellhousing, or a modified upper housing from the R154 used in Japan in conjunction with the 1JZ-GTE. Custom driveshaft, custom downpipe.. I can go on. But it has been done so it is definitely not impossible.