Do established Oakleaf hygrandrea like peatmoss at the beginning of growth season?
Pure peat moss as a top dressing actually repels water if it dries out. Several inches of compost should be adequate with or without some peat moss. The advantage that peat has over compost is that is dries out more slowly and breaks down more slowly. Compost needs to be replenished annually. If your concern is keeping the soil acidic, there are better options. First, start with a soil test. If your soil is very alkaline, use a garden product to lower pH being careful to use as indicated for established plants. The shrub will do fine in pH 7.0 or lower. Application of Hollytone or other fertilizer for acid-loving plants may suffice to keep soil within acceptable range.