Yes, but make sure the crowns are above the soil level.
I use lucerne as it feeds the soil as it breaks down.
I always put straw around the plants once the fruit has set and are starting to swell. As the weight of the fruit increases it will want to lay on the ground which is where the fruit could rot when in contact with the soil. Also, some say that the straw deters slugs and snails but I’m not so sure. Once the fruit starts to grow cover the plants with netting to stop the birds from eating your nice red strawberries. Other pests like mice may fined your fruit irresistible but I have found from experience that their forages into the strawberry patch are few and far between. My own plants have a bumper crop of flowers on them this year so I look forward to good harvests to come.