To a point, yes, but big vines will pull it down or make it lodge easier in a storm. That is how big ag farmers plant field peas and flax and keep it off the ground so they can use a combine to harvest it.
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I'm going to say no. Barley doesn't have any strength and it doesn't grow very tall. so a climbing pea that can hit 2m is not going to find it any use at all, even a pea at 70cm is going to swamp it. just grow short peas 40cm ish and you don't need anything to keep them up, that is the type grown commercially.
Certainly here people do not plant peas and barley together, unless they are using it as a cover crop and the whole lot is going to get ploughed under.
Doody calls. I would really rather that it didn't. Comfort me wise and sterile tiny ad: