Only if it's a swap file on a filesystem on that LVM partition, and even then if the filesystem is otherwise empty then there's no other data to accidentally overwrite, you might just trash the filesystem structure.
Then, if I'm understanding this correctly, the default setup in Ubuntu (at least in Ubuntu 20.04, which I happen to have installed on a couple of laptops recently), which has been mentioned both in this discussion and in the lwn.net article discussion, should be safe from the bug, since that setup, if you enable full-disk encryption, sets up two LVM partitions, one for root (called "vgubuntu-root") and one for swap (called "vgubuntu-swap"). They show up as separate LVM partitions in fdisk. The swap appears to me to just directly use the "vgubuntu-swap" partition.
