I have a leaflet map initialized with EPSG 3857. I need to add new WMS layer that has projection EPSG 2320. I checked proj4leaflet; but I'm not sure whether a layer that has CRS different than main map's CRS can be displayed. Is it possible?
No, it's not possible to have a EPSG:2320 WMS layer in a EPSG:3857 Leaflet map.
Leaflet is not capable of on-the-fly raster reprojection.
You can, however, use EPSG:2320 as the display projection for the whole map (which means not using EPSG:3857 at all).