Nope, titanium is too light for the job. Any crosswind plays hell with your accuracy, and you need the weight of steel to ensure sufficient penetration.

To really be able to answer the OP's question, we'd need a little more info: what century does the katana being used to attack the carbon frame originate in? The ones from pre-eleventh century don't work nearly as well to cut through armor as the ones from the 14th or 15th century, though they are easier to handle.