Hi,
Have you checked, drained the fuel water separator? I suggest that should be the first move for diagnosing this type of problem.
I'm no Honda Fuel Injection expert but no, I don't think squeezing the primer will push fuel from the fuel rail.
The primer bulb feeds the low pressure fuel pump and will fill the VST (Vapor Separator Tank) until it gets full. The float inside the VST will then rise and shut off incoming fuel.
The high pressure fuel pump that is part of the VST feeds the fuel rail and injectors but it doesn't pump fuel unless the ignition is in RUN.
BE CAREFUL testing the way you're doing this because, if you switch on ignition and the pump runs, gas is likely to spray EVERYWHERE from the empty injector hole and that could ruin your month!
A better way to check high pressure flow might be to disconnect the fuel line at the pressure regulator and place the end in a clear container. If you cycle the ignition to on or run BRIEFLY the pump will push fuel. But still be cautious about.this because of the fire danger aspect.
If you're getting fuel to the regulator, it highly likely that the fuel rail and injectors are being fed.
If you want to verify that the fuel primer is charging the VST tank with fuel, I believe that there is a drain screw or plug on the VST that you can open to check for contaminates/water and empty the tank. Once empty, repeatedly squeezing the primer should result in fuel coming from the drain.
Good luck with it.