Maybe, but I don't see how a fence right along a river bank would work from purely engineering perspective. You need to be able to access it easily for repairs, maintenance, etc, and that requires access roads on both sides of the fence.
Yeah, plus the Rio Grande isn't like eastern rivers where the flow is pretty steady- it's flows can vary tremendously, from nearly dried up to ranging floods. A fence near the banks could be high and dry one season, and under water the next.