I don't know anything about Mint. I know it is based on Ubuntu though right? I would say that if you install the Mint version that is the analog of Ubuntu 16.04 my guess is it will work out of the box. Most of this has to do with the drivers that are now upstreamed to the version of the linux kernel that ships with Ubuntu 16.04. I myself plan to do a fresh install of 16.04 without any additional changes.

That's just my guess.

Mint 18 should be coming out in May/June, and will be based on Ubuntu 16.04 LTS. Ubuntu 16.04 does not seem to be out yet.  

Once you do the fresh install, would you mind confirming that everything works as it should on Ubuntu 16.04?

More in general, does anyone know what would happen if I installed Linux Mint 17.3 "Rosa" (kernel 3.19, xorg 1.17, mesa 10.5.9), which is the latest version available (based on Ubuntu 14.04)?

I'm currently running it on XPS13 9350, it is ***. 3.19 kernel doesn't work with the wifi chip from Broadcomm, and updating to 4.4.1 doesn't solve anything, and moreover causes bugs with the display (i915 issue ?)

That's why they used another chip from Intel on the new developer edition.

Update: While I wait for Mint 18/Ubuntu 16.04, I decided to install cinnamon within the Ubuntu 14.04 version shipped from Dell using:

sudo add-apt-repository ppa:embrosyn/cinnamon

sudo apt-get update && sudo apt-get install cinnamon

Installing after a factory reset worked without issues. I was experiencing (even before cinnamon) some random freezes that (so far seem to have) got fixed when I updated the BIOS, but I am still having segmentation faults from lshw (see related thread).