I'm not sure how thick it is, and I can't find it anywhere on the Apple site or elsewhere.
You could try opening the rear slot where you would upgrade your memory and seeing if you can tell from there. There's more about that in this manual, especially about doing it safely:
http://manuals.info.apple.com/en/MacBookPro15and17-inch_Core2DuoUserGuide.pdf
But one piece of advice would be, if you haven't already, to buy yourself a Security Cable that can lock around something foxed and then into your MBP's Security slot. It's the safest way to use your MBP in public without worrying about letting it out of your sight.
MacBook Pro 15" Mac OS X (10.4.9) iBook G4 14", Airport Extreme, USB hub, SeaDisk 320 HDD, Epson R300, Epson RX620
