I've had several that were stuck from gummed up gas residue. I used aerosol can carb cleaner to clear them and then ensure they would only flow in one direction. What are you using for the soak?
I've never had to do it. But, some have yanked that plug out to access the little ball and clean the cavity.
I don't like pulling that square plug. I think it's pretty hard to do without causing damage. I believe they are nylon plugs, though. So, it is possible to make a replacement plug, if you can get some nylon material to shape.
On the PD carbs you can assemble the pump onto the bowl, put some gas in in the bowl and actuate the rod to test pump function, before putting it on the carb. Best to have eye protection if it is working.
Cheers,