There's no "might do" about it. That is what does happen. It has been experimentally established.
I also don't think relying on the Helium-3 / Deuterium reaction is a practical solution because it doesn't really address the problem. When you are talking about reactions that are only sustained for a couple microseconds, fine, starting off with a primary reaction that produces no high-energy neutrons might make sense. There's hardly enough time for the daughter reactions to kick in. But, I don't know anyone daft enough to suggest that microsecond fusion "pulses" are a viable way to produce power. They are great for studying fusion and plasma behavior in a lab environment, but a sustained reaction is what is needed for a practical power source.
What we really need is some way of directly addressing the high-energy neutron problem, because I see no way to side-step it. In any steady-state reaction, regardless of your initial fuel, you are going to end up having the reactions with the highest cross-sections take dominance in a very short period of time. That means you are going to get a lot of high-energy neutrons, period. Better shielding is theoretically possible, but that still doesn't address the fundamental problem that those neutrons are carrying huge amounts of energy out of the system. That's energy we need to capture. Ideally, not just capture but keep within the reaction itself so it can be self-sustaining. None of the current approaches are capable of achieving this.
Unless someone figures out a way to reflect neutrons or persuade the plasma itself to absorb more of them, I cannot see fusion except as a very interesting (and expensive) science project.