Yes, and it's not just about application-level integrity. The WAL operates at a page level, so dropping one WAL entry and then applying later ones would be likely to cause corruption at the B-tree level.

For instance, say you have a node A which has a child B:

* Transaction 1 wants to add a value to B, but it's already full, so B is split into new nodes C and D. Correspondingly, the pointer in A that points to B is removed, and replaced with pointers to C and D.

* Transaction 2 makes an unrelated change to A.

If you skip the updates from transaction 1, and apply the updates from transaction 2, then suddenly A's data is overwritten with a new version that points to nodes C and D, but those nodes haven't been written. The pointers just point to uninitialized garbage.