The containers will still need drainage holes to let out water from heavy rains or watering.
If you are growing in containers you have to try to mimic the properties of soil with soilless potting mix. The container acts as an impenetrable compaction layer that will hold an excessive amount of water like a tub. Soilless mixes are structured to compensate for the lack of drainage and may still benefit from compost. The containers will still need drainage holes to let out water from heavy rains or watering. Many mixes also have water holding particles to help reduce the amount of supplemental watering needed. This can get tricky in spring when the rains are heavy and the roots are small, because the mix will not favor air spaces for the roots to grow. Always remember: roots before shoots.