Fridge will pull about 30 amps from the battery when operating. Yes the alternator should be able to provide that level of power. Typical fridge once cooled is on 40 minutes off 20 minutes so the alternator will have some time to catch up as needed.
I recommend a
GoPower 600 Watt sine wave inverter.Get a small transfer switch such as
KISAE 20a or 15 amp.Mount the inverter close to the power distribution panel. Use the main battery feed for 12v power. Connect the transfer switch to just the fridge branch circuit. Attach a remote power switch. No pulling wire, just make connections. No hassle instant power that anyone can use. No connection to water heater, A/C or microwave. Might power some other convenience outlets to charge small items on the road.