Works if you have some other value to offer. Your example of multi-day is good, but many airbnb accommodations have "cleaning fees" which effectively make multi-day stays cheaper per-day. If you combine it with being already very well verified/reviewed there is a "security" incentive for the host to take you vs another less scrutinized guest, so that's definitely a good leverage. (sure airbnb offers insurance, but who wants to go through that??)
If you want a discount send a long message, introduce yourself, describe your trip length and purpose, come out as nice, explain what your budget constraints are and make a concrete proposal of how much you want to spend. This increases your chances a lot.
(source: I negotiated prices, and also host on airbnb)