Looking at the docs linked from that site, the IPC involves creating a websocket connection to 127.0.0.1 with one of a number of well known ports:
https://discord.com/developers/docs/topics/rpc#connecting
A snapped client should be able to access that fine if it has the network plug connected (which should auto-connect). As a TCP socket, the snap sandbox shouldn’t be a problem.
You should be able to see if the Discord app is listening by running netstat -lt, and look for something listening on localhost on a port in the range 6463-6472.