This would be awesome. There is another discussion going on about this topic here Active Timeline, in My Week, for a task due at a later week & Week Column Not Populating My Week section
In our use case we work in sprints of 2 weeks and most items in our sprint boards do not have a deadline column, but should be dealt with in those two weeks. Because of this they are not popping up the the My week section. Therefore the My week section is totally not used in our company which is a shame.