I think most students will have a natural understanding of logic up to a point. The issue is whether it is sufficient and when and how such understanding needs to be strengthened and formalised through teaching. Perhaps a suitable starting point is to consider the application of logic within a specific science context. This could be formalised in a questionnaire to assess students' natural understanding.
Two suggestions for where to begin:
The logic of real arguments by Fisher
The simple proofs of arithmetic by Epp (discrete mathematics with applications), e.g. the sum of two even numbers is always even.
Without any doubts. I even had to include in my course on the methodology of science for undergraduates the basics of logic and theory of argumentation. Otherwise you will not cultivate a culture of scientific research and a culture of writing scientific texts.