Not no byproducts, but significantly reduced. You can't control side reactions, however unlikely they are. B11 + He4 (the expected byproduct of p + B11) = N14 + n. There's also a rare p + B11 = C11 + n to watch out for as well.

It's a massive improvement on every reaction shitting out neutrons though, and because the main byproduct is a charged particle you can use direct energy conversion instead of going via steam which means the energy output threshold for viability is around 60% of what it would be otherwise.

*C11, not C12 sorry. That then decays with a half life of 20 minutes back into boron-11.