Yes normally AA will send the bags out earlier. However, if this is all one ticket and you simply miss the JFK/DCA segment your CX flight might be canceled. If you are going to do this you need to call AA (was the trip booked with AA).

Second, I highly doubt they will put you on one of the shuttles. If JFK is backed up because of weather so is LGA. Moreover, AA will usually not accomodate to another carrier in the event of weather.

Why don't you simply go standby earlier to JFK (with your bags) if the weather looks bad.