Parameterless templates seem to always be cached, regardless of the presence of dynamic functions within them.
As a simple example, install the DynamicFunctions extension from https://www.mediawiki.org/wiki/Extension:DynamicFunctions and create a new template, DieRoll, whose contents are simply {{#rand:1|6}}. Now, call {{DieRoll}} repeatedly from the same page. As added proof, add a dummy parameter and observe that the template is no longer cached (as noted on https://bugzilla.wikimedia.org/show_bug.cgi?id=30425) and that DieRoll is now random, as it should be.
If this can't be detected directly, I'd like to suggest adding a new magic work, like DYNAMIC that will force the MediaWiki not to cache a template.
(Tested on 1.21.1, but I assume this hasn't changed recently.)
Version: unspecified
Severity: normal