Depending on what you mean by vectors, yes. I don't know how it, if at all, it would apply to svg files, but you can absolutely take a vector and take its Fourier transform, and only keep the first few components to get a compressed representation. That is one way to do image compression.

My (poor) understanding of existing compression techniques is that you have to know what frequencies are OK to discard, otherwise the amount of information remains the same. For things like mp3 or jpg, this depends a lot on human perception of sound and images.

I fear that by dropping high frequency components, the result becomes visually unappealing (such as lines being parallel in the original becoming extremely wiggly and non-parallel).

Maybe OP can make an example with high frequencies removed?