Yes. The cord that plugs into the Strat has a ring and tip. The tip (IIRC) touches a wire on the output jack that goes around in a circuit through all the electronics of the guitar. The ring is attached to another wire that goes through the body of the guitar to the back where the trem springs are. Every Strat has this wire soldered to the anchor that is screwed into that cavity to hold those springs in place. Everything in that assembly is metal, so the springs attach to the block which attaches to the bridge which are in contact with the strings which conduct electricity.
You are missing the fact that inside the guitar, there is a ground wire which goes through the body of the guitar and connects to the guitar’s bridge. On most guitars that I have seen, the wire comes up through the body and the end of it is stripped and wrapped around one of the screws that holds the bridge in place.
I couldn’t find a good picture of this on the web, but I did find a picture of a disassembled Fender Stratocaster:
http://gregboyd.com/images/instrument_images/364_1957FenderStratocasterGuitar_Body.jpg
Note that there are two black wires going into the guitar body. The black and white wires together go to the 1/4" jack. The other black wire goes to the bridge.
ETA: I see that Nunavut Boy said the same thing while I was grabbing a coffee. I should learn to preview.