I am afraid that is very unlikely unless you configure them by yourself. You see, there is (presumably) system-wide date/time format setting already:
$ locale | grep -i time
LC_TIME=en_DK.UTF-8
Nevertheless, nor Mate DE file manager Caja nor GNU ls do not obey that setting automagically. Caja default date format for folder list view is selected through its Preferences menu and ls date format is governed by environment variable. Say, mine is
$ env | grep -i time
TIME_STYLE=+%Y-%m-%d %H:%M:%S
...
As far as I can see, the explanation is that Linux is not monolitic by its nature. Linux distributions are assembled from software pieces produced by ultimately independent developer groups or persons.
Surely, Linux ecosystem as a whole has adopted some de-facto standards, say, filesystem hierarchy standard or freedesktop (XDG) specification. However, decision of following them or not (besides ensuring general compatibility) is at developer’s whim. E.g. one can easily find out that mainstream distributions do not follow FHS scrupulously. That is it.
Yeah @ugnvs there’s no single knob that ties GUI file managers to ls output because they’re built by different upstream projects with their own config systems.
LC_TIME from the locale only covers the format strings glibc exposes, and most apps either ignore it or override it with their own preference.
TIME_STYLE env var is probably the closest thing to a universal switch for coreutils tools. Exporting it in /etc/profile.d/ gets you consistent ls behavior across users.
But Caja, Nautilus, Dolphin, Thunar etc all roll their own date rendering through GLib or Qt.
For ls -l style timestamps everywhere, dropping something like TIME_STYLE=+"%Y-%m-%d %H:%M:%S" in /etc/environment and then matching that format in each file manager’s settings is about as close we can get without writing a wrapper.
