Board Thread:Questions and Answers/@comment-6296810-20140622193753/@comment-5398287-20140622201901

Well, I can't really answer the first part of your question, but as for the second part, no, they can't. There have been quite a few times in the mange and anime where a Shinigami has been disarmed and unable to get their weapon back by thought (like Sora can with his Keyblade), or where they've simply forgotten to carry it with them.