Of course you should show students, taking into account their backgrounds, that the material they are learning in one course is relevant elsewhere. It makes it clearer to the students that topics they are studying have wide usefulness. At the same time, if you know the students don't have a background to appreciate the technicalities coming from other disciplines (not everyone in algebra has had algebraic topology), then you may have to restrict yourself only to making some broad general remarks, although maybe one or two special worked examples from the other disciplines would be accessible without a lot of machinery.

When I discussed characters in an algebra course, I explained a little about Fourier series both for context (otherwise the concept can seem rather far-out) and so they'd see that the otherwise idiosyncratic theorems on characters are related to properties of Fourier series.

I don't think such discussions in a first-year course are going to make the students better researchers, but it will make them better appreciate what they are supposed to be learning.