Hi @Alexander, you've got great timing!
I filed an issue at https://github.com/opendatakit/aggregate/issues/290 a few days ago to remove this publisher from Aggregate because I don't think anyone uses it and I think your post confirms this.
The REDCap publisher was added years ago, and the most detailed documentation we have on it is at https://github.com/opendatakit/opendatakit/wiki/Aggregate-Publishers-Implementation-Details#redcap-xml-publisher. The latest information about whether or not the publisher works is at REDCap To ODK - #30 by Mitch_S. In that topic from March 2016, Mitch says..
A RedCap publisher was contributed many years ago.
Upon later testing, it was discovered that the RedCap server requires a specific ordering of Header fields in requests sent to it (this is a non-conformance with HTTP protocols). This may or may not have been fixed. If it has, then everything should work. i.e., give it a try.
If it has not been fixed in the RedCap source code, then you will need to work with RedCap developers to fix their server implementation.
REDCap is only available to institutions who join the REDCap consortium and that makes it really hard for the ODK community to engage with their team. If you belong to the consortium, perhaps you can ask the REDCap developers if they could test the publisher?
If it works and people use it, great, we should keep it. If it doesn't work, I'd love to remove it in the next release of Aggregate.