No, you will have to create particles each step and define the positions manually. You'll probably find it optimal to initialize an array full of a bunch of random points within the curve in a create event and then create your particles at a random point from the array.
There is no curve emitter. I would probably just use part_particles_create() with lengthdir_x/y. The dir would be a random_range between your curves start and end arc with the len matching your curve requirements.