Asparagus crowns tend to be available for short windows of time (in early Spring and in the Autumn) from growers, and the BEST way of planting them is to get them in the ground as soon as you can after you’ve bought them. So the answer to whether you can plant them in the summer is, well, you’re unlikely to be able to get hold of them to do that. The primary reason for planting in the Spring is so that they get the the warmed soil and the summer to establish themselves, so late Spring would be ok if we’re having a bad year for weather.