There are 2 types of sand scratches that show up. There are sand scratches, as you said that show up in the base coat from not sanding fine enough. These sand scratches will show up immediately when you put the base on and will be visible. Usually 400 grit is fine enough, however, I like to go 600 wet, for the added insurance of not getting sand scratches and I can get a better reflection in 600 wet to make sure the car is straight, compared to 400 dry.
The other type of sand scratch happens when to coarse a paper is used when doing body work and the primer is expected to fill these scratches. The primer does go into the scratches, but, the primer will top cure and trap the solvents that are in the primer and the solvents aren't released as the top cures. The car is sanded and top coated with base coat. After the car is cleared, the solvents in the base coat and the clear coat, go down through the primer and release the solvents that are in the sand scratch. As the solvents that where trapped in the sand scratches that where filled with primer are released, there is a void where the solvents where, causing the original primer substrate to sink, leaving a sand scratch that shows up 6 months to a year down the road.
So, the moral of the story is that it's very important to finish sanding with the proper grit to endure that you don't get sand scratches in your base coat and to finish your body work with fine paper so that the primer that your using doesn't lay down deep in the coarse scratches, not totally cure and give you trouble months down the road.
Hope this answers your sand scratch question...if you need any more clarification, feel free to ask, I'll try and explain further.