If you power the hub, I fully expect the mouse to work.

With an unpowered ("bus powered") hub, it's more of a crapshoot: each device, including the hub, advertises it's power needs to the host, and the total has to be small enough to accommodate whatever the root hub (in the PC) advertises that it is capable of (normally 500mA).

It is quite possible that the hub, and/or the mouse, advertise a higher number than they really need. Edit: And the hub itself will normally advertise different values when self-powered than when bus-powered.