I have a couple sets, a few training races, raced this past season on one set, (303 rims) I also use them during the road season. I have smacked my share of hidden roots and have felt the cross tires bottom. No damage.
I would never run a set of the carbon clincher (carbon bead version) as a cross tire. Too many impacts on a carbon ridge. If is the alu. braking surface Zipp, my opinion would be different, but then would question why the clincher when the tubulars are far superior when it comes to cross.
The 404's are good wheels. I would make sure that if they are not the newest version, that they have the cross layup (extra layer in impact region). The Reynolds Stratus are a bit more beefy when it comes to impacts though.