What will happen to swap partitions after upgrading to Ubuntu 18.04?

According to 18.04 Bionic Beaver release notes:

For new installs, a swap file will be used by default instead of a swap partition.
Changes since 16.04

What will happen to the existing swap partition after the scheduled upgrade in July from my current Ubuntu 16.04 to Ubuntu 18.04? Will it still exist? If so, will it be used, or just take up dormant space?

For distribution upgrades, the existing swap partition will be reused instead of creating a new swap file. In your case the existing swap partition from 16.04 will remain unchanged and be reused in 18.04.

You can share swap area with two or more operating systems. To share swap space, create the swap space when you install the first operating system and then when you install the second one, do not create a new swap space, instead just use the first OS's swap space as the mount point for swap space of the second OS.^source

For an explanation about the differences between a swap file and a swap partition see this answer.