Comprehensible Input is important - but even more important, I think, is input per se - whether comprehensible or not. It is the sheer volume of material that helps your brain get to grips with new structures and word /sound patterns that are not present in the native language morpheme set. One needs to re-hear, or be re-exposed to sets of language data many hundreds of times for the information to become hard wired in the brain.
I suspect it is the INPUT aspect of comprehensible input that is the most important part of Krashen's method. Obviously, more pleasure is involved in taking in that input, if there is comprehension.......but comprehension will come, as long as there is context (either provided in realia, or via translations or other more or less artificial methods language teachers use such as acting out, TPRS etc etc)
After all, "colourless green ideas sleep furiously" is perfectly grammatical, but meaningless. Meaning is not required for information to be extracted.
I would encourage your students to listen to hours and hours of Latin outside of class time, and there are increasing numbers of sources online for doing so.
Encourage them to keep a log of their language listening. Indeed, you could even make this into a class enterprise. It would then be interesting to see if you can correlate results with number of hours of audio input reported. This could be the makings of a nice little academic paper.