Is a new refrigerator likely to trip a 20 amp AFCI/GFCI circuit?
I can tell you this has been an area of discussion among the electrical community for a few years. The problem being some appliances built before the insertion of AFCI requirement do not work well on those types of circuits. 

Most equipment built after 2008 should be able to be installed on the new requirements and work well. You might check with the manufacturer and have them point out where in the warranty it shows that their appliance is capable to meet the newer codes.

Good luck.