If the driver for macOS is available for the touch screen controller used in your display, then it's no problem. I've done this many times in the past, but not specifically on Mojave. So in general it can be done, but if it doesn't work there is very little you can to do make it work. There are absolutely no guarantees.
Elo basically uses 3rd-party drivers from touch-base.com
From what I see, it looks like that the UPDD v6 (latest) drivers support virtually all the various of Elotouch monitors. Which is good, because they are awful about listing which specific controller exactly is used in which specific model number. These are semi-universal drivers essentially, and they do work in High Sierra 10.13, so that's pretty encouraging (but no guarantee) they will work with Mojave 10.14.
The fact that you're running a Mac Mini doesn't really matter, it's all about which version of OS X or macOS you are using.
To be reasonably sure I would email them at technical@touch-base.com to find out if their UPDD v6 drivers work on Mojave (if that's what you have), or not. If they claim specifically that it's been tested in Mojave, then great! If they just say it works on whatever-old-version "and above" that's totally meaningless.
Here is a great simplified guide on how to install the drivers:
https://slatemt.zendesk.com/hc/en-us/articles/360001548048-Touch-not-working-on-High-Sierra-No-Registered-Devices-
Their official touch-base.com guide is one I find very painful to read and adds very very little useful info and buries the important information at the link above, but here it is:
http://support.touch-base.com/Documentation/50334/Mac
Since they do work in High Sierra most likely they still work in Mojave, but you have to consider if you're willing to take the reasonable risk they won't and if you'd be able to return your ELO or not.
Hopefully someone here has had affirmative recent experience using UPDD drivers w/ Mojave, but that's extremely not common.
Lastly, keep in mind that macOS 10.15 Catalina coming out this fall supports "sidecar" which is a feature that let's you use an iPad as an extended monitor with touch screen for macOS:
macOS Catalina - Features - Apple
Along those lines, even if UPDD works with Mojave there's even less guarantee they will continue to work with Catalina. So even if you get the ELO working I would only go down this road if you are prepared to stay on your current macOS and perhaps may not ever be able to upgrade. This is another factor to consider.
That being said, I have always loved ELO, they are the best in terms of touch screen monitor hardware.