Based on my experience with 14.04 and 16.04, the HWE kernel doesn't "upgrade" other packages, but it may enable performance improvements other than simply supporting hardware that came out after the initial release of the LTS version you're using.

For instance, I found in 16.04 that I got a significant improvement in computing speed as seen in more rapid completion of BOINC distributed computing tasks.

Essentially what you're getting with the HWE kernel is a newer kernel revision, incorporating all the improvements made to the kernel between the one you're running and the one that carries the HWE label. You're not getting newer versions of any other packages, unless there's an upgrade or backport that specifically requires the HWE kernel version.

No

Upgrading to newer kernel using HWE does not upgrade any other software. In general the other software that get installed with Ubuntu don't get upgraded during the life of that version of Ubuntu except for security reasons. Firefox get updated for this reason.

So, you will not get a newer version of LibreOffice or Shotwell if you install HWE kernels.

Hope this helps