In short, yes, this (should!) just work. I have a 2012 that over the years has run headless, with dvi extenders and at the moment has only a remote Displaylink monitor. Ran a 20” cinema and it now runs a 4k screen (30hz). There is a performance hit but it works fine. I run Mojave, Displaylink is choosy about OS and drivers (and with every new OS apple breaks it)
you might also look on the Displaylink forums, used to be an active Mac section there.
mine does auto login, perhaps try that and see if that’s the trick.