Should be (more or less) possible - with at least one caveat.
While the API can (with RoI) read the chat panel, it can't write to it. So as long as the leader has this plugin, and the other members either manually type in DKP: <bid> or assign it as an alias, everything else should work fine.
If you combine this with some form of DKP plugin that allows players to keep track of kin DKP, you could even have some validation to make sure that what a player is bidding is actually possible.
Unfortunately, such a DKP manager would have to be manually kept up to date, as there's no way of accessing the web via the API.
Note: I'm not volunteering - if you could see my current to-do list, you'd understand why. I'm just "fertilizing" your idea so-to-speak, by confirming that it is possible, as well as contributing some additional ideas into the mix
