Shawn, you should know better than to be so sloppy as to say "velocity of particles is temperature". Since the particles all don't have the same velocity, do you take the arithmetic mean, the geometric mean, the root mean square, the most probable...which one?
In any case, equation (8) from your first wiki link has the rigorous definition of temperature (which I mentioned in the first half of my second sentence above), and the two quoted parts are exactly what I said in the second half of that sentence.
To attempt an answer of the OP's question: Empirically, we see that a varying acceleration does affect kinetics (at the very least, in reactions that are rate limited by diffusion) as is often seen by shaking a reaction beaker. The effect of a uniform acceleration is more tricky. There can be different regimes and different factors to consider depending on the phase of the system and the reaction mechanism. There might be an interesting transition during acceleration when you go past the speed of sound in the system. Much below this speed, there may be little happening, as the system equilibrates faster than the box moves. Above this speed, the system may be in a significantly non-equilibrium state. For a gas phase system, this will probably show up as a pressure gradient, which will affect the kinetics through the partial pressures in the rate equation. Also, a second order effect is that the work done on the system by the external force might induce a change in internal energy (hence, temperature).