Is it appropriate to put a scientific/technical document about code developed by our group on arXiv?
If your manual is specific to your group's environment (software, lab, equipment, protocols, etc.), then I would consider posting such document on arXiv as not appropriate. A better place for such documents IMHO would be figshare or Zenodo. Both services allow artifacts to be not only citable, but also discoverable (via DOI assignment). Version control is supported as well, but the advantage of Zenodo in this regard in comparison with figshare is Git and GitHub integration.

If, on the other hand, the document is not specific to your group's or other particular environment (or, perhaps, you want to share this document as a model of how such documents should be structured, presented and what content should they contain), then I agree with other answers in that it is totally appropriate to post such document on arXiv.