An example of the effect I'm going for can be found here, with the particles going into the brain. They have a glow around them, and a small tail behind them which has a sort of falloff.
yes, you can model a mesh to behave exactly like you described, then assign that mesh to the particle.
To make them glow you can assign a surface emission material or volume emission material and you can even blur anything that moves to give some realism.
But if you want to have the same effect as in the video, then you can get away without using particles. Just constrain the mesh to a curve and animate it.