I've ridden on some unpaved roads that are similar to the one in the picture on a road bike with standard 23 mm tyres on. Slippage is only an issue if you're forcing the pace and accelerating out of the saddle. If you're seated, and you probably will be, then I very much doubt you'll have any problems.
As above.
Stage 16 Giro 2008 tech:
http://www.roadbikeaction.com/fly.aspx?layout=content&taxid=71&cid=280