Can the OS X Mail dock count be made to show all (not just unread) count of inbox?

DockStar solved the issue for me. It now has an update to support both Mavericks and Yosemite when it comes out. I only tested in on Mavericks though, works great.

The great thing for me was that I have exactly 4 inboxes, so I can add a badge for all of them.

I managed to find a workaround: I have an AppleScript running every 10 minutes on my machine to set ALL my Inbox emails to status: unread. This updates the Dock badge icon. Since I follow the Inbox Zero philosophy, I don't care if emails I've read get marked unread.

tell application "Mail" set read status of every message of inbox to false end tell

I run it every 10 minutes on Mac using this excellent lanchd scheduling tool: LaunchControl by Soma Zone software.