Asparagus is fairly tolerant to a variety of soils, but does like sandy loam. If your plants look healthy, it might not be necessary to add the loam. If you do decide to try it, however, you might set the depth at 2 to 3 inches instead, to be sure not to damage any shallow roots. Or, if you have a small enough bed, gently work the loam in at that depth with a rake or shovel. As you have indicated, the plants should be dormant when you do this. Some gardeners instead add aged manure or compost in fall, along with a layer of mulch, which will gradually improve the soil structure and health. Others might work in soil amendments in early spring, before the spears appear.
Asparagus is fairly tolerant to a variety of soils, but does like sandy loam. If your plants look healthy, it might not be necessary to add the loam. If you do decide to try it, however, you might set the depth at 2 to 3 inches instead, to be sure not to damage any shallow roots. Or, if you have a small enough bed, gently work the loam in at that depth with a rake or shovel. As you have indicated, the plants should be dormant when you do this. Some gardeners instead add aged manure or compost in fall, along with a layer of mulch, which will gradually improve the soil structure and health. Others might work in soil amendments in early spring, before the spears appear.