I feel that a 3/8” suction hose is a bit small, but with the right atmospheric air intake it may work ok. You need a steady stream of air being sucked through the media hose, then media dribbled into it at a constant rate, whatever that takes to get it.
On my custom gun that I made, note that there is no barb fitting at the base of the gun. I use a 5/8” inside diameter automotive heater hose for the suction hose, and the O ring in the handle gets compressed onto the outside of the hose by the knurled ring to seal it. On my media mixer, it is a 3/4” nominal hard pipe ******, cut in two at a 45 degree angle, rotated, then welded back together to turn the corner. There is an air hole on top of the fitting to allow intake air, and the hose just push fits into the fitting the amount required for a good media/air mix through the hole. It is a grit “carburetor”. There is a tapped hole for a set screw, but I found it was not needed due to the nice fit of the hose into the mixer.
The hole needs to be relatively close to the corner of the fitting so grit laying in the fitting gets pulled by the air stream. Too far away, and the grit gets a chance to pile up and create a rich mix. The base of a gun can be drilled and tapped for a larger fitting for more grit flow.