Compression vs. redundancy: do they cancel each other out?

Does it make sense to compress a tarball (or any kind of file, really), e.g., using gzip or bzip2, while at the same time creating redundancy files for it, e.g., a par2 file? The context is that I am reasoning about how to best backup my personal files. My #1 priority is to avoid data loss due to bitrot, hence, the par2 files. Compression would be nice but is not my main concern. The reason I am doubting the combined application of a compression algorithm and a erasure code algorithm is that the former works by eliminating redundancy (thereby creating smaller files) while the latter works by adding redundancy (thereby adding the capability to perform data recovery operations). Don't they cancel each other out? Is this a reasonable assumption or am I missing something here?