As other have said, you don't need to solder, but I would at least tack separate pieces of foil together with solder. The reason I say that is that people have told me (I haven't used the Stew Mac conductive adhesive) that after some years (4-5?) the glue dries out and looses it conductivity. So at that time you'd have to solder it or replace the foil. So I'd say just tack the separate pieces with solder to each other in a couple of spots so that if the glue does dry out, the shielding will still be connected.
A+ on the SX. They all need shielding. You can see a picture of some of my SX shielding over in the pickups and electronics forum. It's under the SX pickup switch mod subject. Note how the copper comes up over the lip of the rout so the metal plate makes contact with the shield when you screw it down. Note that the copper is connected to the circuit with a wire (yellow) to the ground of the jack. [actually it goes to the back of the tone pot which goes to the jack ground]
Note that I soldered all seams on mine to make the shield "watertight". That is really extreme and not necessary. A few evenly spaced "tacks" plus the conductive adhesive should be fine. Good luck.
