Will a free neutron radiate if it is decelerated?

The neutron is magnetic. It is a tiny little magnet. In more formal language, it carries a magnetic dipole moment of size $$ \mu_n = −9.6623647(23) \times 10^{−27} {\rm J\,T}^{−1}. $$ This is what allows it to interact with electromagnetic waves---or, to say the same thing another way, with photons. This also means that when accelerated then yes, it will generate electromagnetic radiation. This effect is much smaller that the radiation of a charged particle with the same acceleration.

You can associate this radiation with the presence of accelerating charge, indirectly, by noting that the neutron has charged quarks inside it, but strictly speaking those components have to be treated by quantum theory so they shouldn't be thought of as little separate charges. The calculation in terms of magnetic dipole moment is more appropriate.