"If I put one pole bean plant every 24 inches will that plant branch out and produce more than 5 plants in the same 24 inches planted 6 inches apart."

Probably not... but that would depend, in large part, upon the variety. Note the single plant of "Pole 191" below:

Less rampant varieties (such as "Fortex", "Emerite", "Trionfo Violetto") would probably benefit from the close spacing. I tested that theory with "Emerite" this year, which has been noted as a relatively low-yielding variety. When thinned to hills of 2@12" (same as one per 6"), it produced a spectacular yield - and is still bearing. Most half-runner varieties would likely give their best performance at this spacing as well.

However, the more rampant varieties (such as "Goose", "Pole 191", "Kentucky Wonder", and "Garafal Oro") might be more than a little crowded. Their optimal spacing seems to be somewhere in the neighborhood of 12" between plants. For beans with the tendency to branch heavily, they will indeed spread out if given space... but 24" between plants would probably be excessive for most pole beans. To me, when planting in rows along a trellis, the optimal spacing for a variety is the widest that still produces an unbroken canopy of foliage at maturity.

As a rule, while the yield per plant will be lower when plants are more closely spaced, the yield for a given area will be higher. This concept works well for farmers, since they need the maximum attainable yield per acre. They are not concerned with size, or quality... only bulk. Smaller ears of corn, for example, don't matter, as long as there are more of them.

For gardeners, though, aesthetics matter. We want the largest, the most attractive, the most flavorful. For snap beans, crowded plants might produce more, but smaller, pods. I personally prefer the results of wider spacing, since it allows each variety to exhibit its true potential, and because I believe it produces larger & stronger seed... but if space is limited, that may not be an option.

Yield aside, there are other considerations for pole bean spacing:
- Beans are more prone to disease when the foliage becomes dense enough to block airflow; so in moist climates, or where disease is prevalent, wider spacing may be advisable.
- Since close spacing may stunt the vines, it may be a desirable tactic if growing pole beans on a relatively short support, such as a 4-5' fence.
- While the yield for a single picking of snap beans may be greater with close spacing, it may be less sustained. Years back, when I planted my beans closer together, I noticed that the vines "tired" soon after the first picking, regardless of variety. They would often bounce back later in the season, after a period of little to no yield... but with wider spacing, I usually have nearly continuous yield.

The overall yield of snap beans for a given area - for the entire season - may be higher for plants given wider spacing; but I have, at present, no data to support this. It would be a really great experiment, but every picking throughout the season (for each spacing) would need to be harvested, weighed, and recorded - a truly arduous task, which is why I have never done it.