Will existing grass grow through topsoil?

Yes, if you don’t apply it too deep.  You can apply a light layer of topsoil, less than 1”, and the grass should come back through it with time.  Use a rake to work the soil down and help the grass stand back up as you apply it.  As, you apply more depth of topsoil it will take longer for the grass to grow back to the surface.  Also, consider the timing of the application as fescue will not growing quickly in the summer and bermuda will not grow back quickly in the fall or winter.  If you need to patch or repair the lawn with several inches of topsoil, you may consider just re-sodding or re-seeding that area and mulching lightly with straw.