The determining factor is the wire gauge from the alternator to the camper's battery. Most likely you still have factory wiring, maybe 10 gauge, possibly 12. Let's be optimistic and use 10 gauge and say 30 feet of it between the alternator and battery. That works out to a resistance of .03 ohms(R). Using Powerdude's figure of 15 amps(I) to run the fridge that means if the alternator is putting out 13.8 volts(E) the most the battery can be charged to is 13.35 volts due to .45 volts dropped across the wire(E=IxR). And that's assuming no stray resistance from wire connectors, the trailer plug, etc., and no other loads drawing current. To make matters worse if your battery is in need of a charge and is trying to draw say 25 amps charging current that lowers the voltage to 12.8. But, as the battery gradually takes a charge and draws less current, that will allow the charge voltage to increase, but never beyond the 13.35 due to the drop from the fridge current.
Now your 100W solar will help, but it isn't capable of supplying all the current the fridge needs so you'll still not get to a full charge while the fridge is on DC. You're probably going to get pretty close though unless you're starting out the trip with a really drained battery.