Will migrating an SSD drive to APFS prolong its life?
Will switching the file system from HFS+ to APFS prolong the life of
  an SSD drive?


No.  APFS was optimized for flash (NAND) SSDs.  In other words, it was designed to fully utilize the capabilities of an SSD to provide better performance.  It wasn't implemented to prolong the life of an SSD.

In most respects, the life will be shortened. Why?  Increased write operations for 


Encryption
Snapshots
Metadata


None of that matters however, because based on the calculated life expectancy of an SSD, you will run out of capacity, long before it dies from usage.  In other words, it's a moot point.


  What other advantages/disadvantages it might bring?


This is entirely opinionated question.  However, one thing to keep in mind is the initial premise of the answer - APFS was designed for SSDs. Meaning it wasn't designed for traditional spinning hard disks.  Quite frankly, I've never upgraded a file system and thought "gee...this new feature is a disadvantage."

So, a better way to look at this is the advantages/disadvantages of running APFS on spinning disks versus SSDs.

For example, APFS on an SSD has encryption at it's core rather than another layer on top of the file system so, it's faster and more secure (advantage).  On a spinning drive, this results in more read/writes on the physical media meaning slower performance, higher overhead, and shorter lifespan (disadvantage).

For an indepth look from a ZFS developers perspective, see this article