Biggest advantage will be the clean cold air, the "ram" effect is quite small unless you are above something like 100mph. Also the ram intake design needs to be good, otherwise it will cause more drag than it adds in power.

If the Crossfire ran a MAP sensor I doubt a RAM could generate anything near positive boost to generate fault codes, but I think the Crossfire runs only a MAF sensor and as HDDP says the ECU will crunch the numbers and control the A/F ratio. Not sure it aims for 14.7:1 at least on the SRT that wouldn't be wiseor help power, but with only narrow band sensors perhaps it does??

edit - noticed from the DTC list that there are codes for MAP sensor so it's there as I say above, ram effect won't generate positive pressure, would be interesting to log the data from it with and without the ram.