I wouldn't use a rack on a full carbon bike. However, you could use the commuter bike for touring -- there's a fair amount of overlap between the optimal setups for touring & commuting bikes.

If you are credit card touring (i.e. staying at hotels rather than camping) and traveling light, you'd be fine with a big Carradice bag and whatever handlebar bag will fit.

However, if you're camping you really will need a rack or some way to carry a fair amount of weight and bulk.