No u can't bolt a 3SGTE to an ST162 box and i don't think that u can do it to the ST182 either. The problem is the the starter motor sits where the turbo goes.
The Boxes that can be used are the sv21 camery box, the MR2 turbo box and the GT4 box(modified). There are problems with each of these boxes. The best box for the 3sgte FWD conversion is the MR2 turbo box, the problem with this box is finding it, all u have to do then is change the linkages. sv21 is a bit weak. GT4 needs to be modified and is the heaviest of them all.
I have done the 3sgte FWD conversion. I put the sv21 box in till i found an MR2 turbo box with an LSD, i pick it up tomorrow.