This is not really an answer to the question but more an eleaboration on my comment.
As far as I understand the way arXiv-trackbacks for MO are supposed to work is (almost) completely automatic, if there is a link to the arXiv it creates a trackback (except if it falls through the cracks for some reason).
To do the same for this network is in my opinion not a good idea, by contrast there should be an opt-in mechanism, by which I mean that the post only shows up there if in some way the post is "marked" in a special way (this could be some non-invasive text-pattern or special way to link, or still something else technically this should be not a problem).
The reason why I think it is not a good idea to send everything over there that happens to link to the arXiv is that this would flood that page with tangentially relevant entries, and in some cases also with problematic ones. There is simply a big difference between making a post that is on some paper, and a post happening to link to a paper. (This remains true if this is restricted to links in questions.)
This also applies to the arXiv trackback in a certain way. But first there are many many papers on the arXiv while there are not yet that many posts on this site, so it is in a relative sense not so much problem, besides these trachbacks on the arXiv being quite a side-aspect while on this site they are the main thing.
So, if we send them many low-quality entries (at least for the purpose at hand) this is seems like a problem.
(Final explication what I mean with "problematic": sometimes certain (not all) discussions of preprints here on MO are critizised as potentially offensive or embarassing for the author, still a track-back is created, as it is automatic, so that everybody looking at the arXiv might stumble over this potentially offensive discussion. This is a slightly strange state of affairs in my opinion. But then these trackbacks are not so visible, but for that other site this is a bit different. In addition, it could also make sense to inform people that what they say here on MO on a paper, will in some immediate way be linked to the paper. It is not clear to me if everybody is aware of this. Of course the license permits it being done, but not everything that is permitted needs to be done, or at least that it is done might be communicated more prominently. To be clear I have not personal problem with any of this, this is only something that crossed my mind on ocassion and also just now, and to explain what I meant.)