I don't think there is any reason for the hand-pump not to share the top feed with an injector, but it may result in not being able to use all three feed methods at once.

I would ask though if a pump adding its output pulses to the injector delivery, possibly at higher pressure than the injector can give, would prevent that injector from working properly.

In emergencies you need all options!

It would need extra clack valve on the top–feeds. A Tee-piece alone would not be enough if upstream from the top-feed clack-valve. You'd need a second clack-valve in the injector delivery, otherwise at least some of the water from the punp would escape through the injector overflow.

For aesthetic reasons, it may be possible to arrange all this low down, adjacent to the injector, but it might call for a pipe size up from that used by the injector alone, and slightly larger top-feed clack-valve, to enable both devices to be used at once.

From the boiler's point of view, feeding cold water into the firebox water-space is not good, though mechanically feasible. You need run a pipe back under the foot-plate to a suitable connection on the drag-beam. If you need install a feed in a back-head wash-out bush, it would be better to route an injector to it and send the pump water to the vacated top-feed. (An injector heats the water.)